In [ ]:
fig, ax = plt.subplots(figsize=(10, 7), subplot_kw=dict(projection='3d'))
ax.plot_surface(x1, x2, y)
ax.set(
xlabel='$x_1$',
ylabel='$x_2$',
zlabel='$f(x_1, x_2)$'
)
plt.tight_layout()
plt.show()
import numpy as np
import matplotlib.pyplot as plt
import random
import pandas as pd
import tensorflow as tf
from sklearn.model_selection import train_test_split
from sklearn.neural_network import MLPRegressor
from sklearn.metrics import mean_squared_error
from sklearn.metrics import mean_absolute_error
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import Normalizer
from tensorflow.keras.layers import Dense
from tensorflow.keras.models import Sequential
from tensorflow.keras.optimizers import SGD, Adam
from keras.layers import Flatten,Dense,BatchNormalization,Activation,Dropout
from keras.callbacks import ReduceLROnPlateau
from sklearn.metrics import classification_report, confusion_matrix, ConfusionMatrixDisplay
Utilize redes neurais perceptron de múltiplas camadas para aproximar as funções abaixo. Apresente um gráfico com a curva da função analítica e a curva da função aproximada pela rede neural. Apresente também a curva do erro médio de treinamento com relação ao número de épocas e a curva do erro médio com o conjunto de validação. Procure definir para cada função a arquitetura da rede neural perceptron, isto é, o número de entradas, o número de neurônios em cada camada e o número de neurônios camada de saída.
Observações: Como se trata de um problema de aproximação de funções, considere a ca- mada de saída do tipo linear puro. Isto é, φ(v)=v, onde v é o potencial de ativação.
$f(x_1,x_2) = (1 -x_1)^2 + 100 (x_2 - (x_1)^2)^2$ com $-10 ≤ x_1 ≤ 10, -10 ≤ x_2 ≤10$
# function's definition
def f(x1,x2):
return (1 - x1)**2 + 100*(x2 - (x1)**2)**2
# generating points
x1, x2 = np.meshgrid(np.linspace(-10, 10, 100), np.linspace(-10, 10, 100))
y = f(x1,x2)
fig, ax = plt.subplots(figsize=(10, 7), subplot_kw=dict(projection='3d'))
ax.plot_surface(x1, x2, y)
ax.set(
xlabel='$x_1$',
ylabel='$x_2$',
zlabel='$f(x_1, x_2)$'
)
plt.tight_layout()
plt.show()
# split training and test
x_train, x_test, y_train, y_test = train_test_split(
np.vstack([x1.flatten(), x2.flatten()]).T,
y.flatten(),
test_size=0.2,
random_state=42
)
fig, ax = plt.subplots(figsize=(10, 7), subplot_kw=dict(projection='3d'))
ax.plot_wireframe(x1, x2, y, linewidths=0.5, color='lightgrey')
ax.scatter(x_train[:,0], x_train[:,1], y_train, s=1, color='darkorange', label='Training data')
ax.scatter(x_test[:,0], x_test[:,1], y_test, s=5, color='darkgreen', label='Test data')
ax.set(
xlabel='$x_1$',
ylabel='$x_2$',
zlabel='$f(x_1, x_2)$'
)
plt.legend()
plt.tight_layout()
plt.show()
# created scaler
scaler = StandardScaler()
y_train = y_train.reshape(-1,1)
y_test = y_test.reshape(-1,1)
# fit normalizer on training dataset
scaler.fit(y_train)
# transform training dataset
y_train = scaler.transform(y_train)
# transform test dataset
y_test = scaler.transform(y_test)
# verifying shapes
print("X train shape: ", x_train.shape)
print("Y train shape: ", y_train.shape)
print("X test shape: ", x_test.shape)
print("Y test shape: ", y_test.shape)
X train shape: (8000, 2) Y train shape: (8000, 1) X test shape: (2000, 2) Y test shape: (2000, 1)
mlp = Sequential([
Dense(64, activation='relu', input_shape=(2,)),
Dense(32, activation='relu'),
Dense(16, activation='relu'),
Dense(8, activation='relu'),
Dense(4, activation='relu'),
Dense(1, activation='linear')
])
mlp.compile(
loss='mean_squared_error',
optimizer='adam'
)
mlp.summary()
Model: "sequential_1"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
dense_6 (Dense) (None, 64) 192
dense_7 (Dense) (None, 32) 2080
dense_8 (Dense) (None, 16) 528
dense_9 (Dense) (None, 8) 136
dense_10 (Dense) (None, 4) 36
dense_11 (Dense) (None, 1) 5
=================================================================
Total params: 2,977
Trainable params: 2,977
Non-trainable params: 0
_________________________________________________________________
history = mlp.fit(
x_train, y_train,
batch_size=8,
epochs=2000,
validation_split=0.1,
callbacks=[
tf.keras.callbacks.EarlyStopping(monitor='val_loss', patience=10),
tf.keras.callbacks.ReduceLROnPlateau(monitor='val_loss', factor=0.1, patience=5, min_lr=0.0001)
]
)
Epoch 1/2000 900/900 [==============================] - 2s 1ms/step - loss: 0.2403 - val_loss: 0.0481 - lr: 0.0010 Epoch 2/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0301 - val_loss: 0.0225 - lr: 0.0010 Epoch 3/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0200 - val_loss: 0.0144 - lr: 0.0010 Epoch 4/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0144 - val_loss: 0.0141 - lr: 0.0010 Epoch 5/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0098 - val_loss: 0.0073 - lr: 0.0010 Epoch 6/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0094 - val_loss: 0.0056 - lr: 0.0010 Epoch 7/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0102 - val_loss: 0.0024 - lr: 0.0010 Epoch 8/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0082 - val_loss: 0.0071 - lr: 0.0010 Epoch 9/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0055 - val_loss: 0.0031 - lr: 0.0010 Epoch 10/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0053 - val_loss: 0.0126 - lr: 0.0010 Epoch 11/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0051 - val_loss: 8.4492e-04 - lr: 0.0010 Epoch 12/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0045 - val_loss: 0.0091 - lr: 0.0010 Epoch 13/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0103 - val_loss: 7.3677e-04 - lr: 0.0010 Epoch 14/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0041 - val_loss: 0.0061 - lr: 0.0010 Epoch 15/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0034 - val_loss: 0.0015 - lr: 0.0010 Epoch 16/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0047 - val_loss: 0.0060 - lr: 0.0010 Epoch 17/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0028 - val_loss: 0.0046 - lr: 0.0010 Epoch 18/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0045 - val_loss: 0.0064 - lr: 0.0010 Epoch 19/2000 900/900 [==============================] - 1s 1ms/step - loss: 3.8528e-04 - val_loss: 3.2380e-04 - lr: 1.0000e-04 Epoch 20/2000 900/900 [==============================] - 1s 1ms/step - loss: 2.4806e-04 - val_loss: 2.2849e-04 - lr: 1.0000e-04 Epoch 21/2000 900/900 [==============================] - 1s 1ms/step - loss: 2.4695e-04 - val_loss: 2.0553e-04 - lr: 1.0000e-04 Epoch 22/2000 900/900 [==============================] - 1s 1ms/step - loss: 2.3648e-04 - val_loss: 1.9860e-04 - lr: 1.0000e-04 Epoch 23/2000 900/900 [==============================] - 1s 1ms/step - loss: 2.3406e-04 - val_loss: 1.8407e-04 - lr: 1.0000e-04 Epoch 24/2000 900/900 [==============================] - 1s 1ms/step - loss: 2.1895e-04 - val_loss: 2.1349e-04 - lr: 1.0000e-04 Epoch 25/2000 900/900 [==============================] - 1s 1ms/step - loss: 2.5439e-04 - val_loss: 2.7080e-04 - lr: 1.0000e-04 Epoch 26/2000 900/900 [==============================] - 1s 1ms/step - loss: 2.3294e-04 - val_loss: 3.1382e-04 - lr: 1.0000e-04 Epoch 27/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.9288e-04 - val_loss: 2.5049e-04 - lr: 1.0000e-04 Epoch 28/2000 900/900 [==============================] - 2s 2ms/step - loss: 2.0941e-04 - val_loss: 1.4517e-04 - lr: 1.0000e-04 Epoch 29/2000 900/900 [==============================] - 2s 2ms/step - loss: 2.0231e-04 - val_loss: 1.7252e-04 - lr: 1.0000e-04 Epoch 30/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.8211e-04 - val_loss: 1.2884e-04 - lr: 1.0000e-04 Epoch 31/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.8255e-04 - val_loss: 1.1797e-04 - lr: 1.0000e-04 Epoch 32/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.5825e-04 - val_loss: 2.3869e-04 - lr: 1.0000e-04 Epoch 33/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.8320e-04 - val_loss: 1.7549e-04 - lr: 1.0000e-04 Epoch 34/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.5552e-04 - val_loss: 1.2200e-04 - lr: 1.0000e-04 Epoch 35/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.6122e-04 - val_loss: 1.1288e-04 - lr: 1.0000e-04 Epoch 36/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.6115e-04 - val_loss: 1.4661e-04 - lr: 1.0000e-04 Epoch 37/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.7000e-04 - val_loss: 1.8074e-04 - lr: 1.0000e-04 Epoch 38/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.5897e-04 - val_loss: 1.3702e-04 - lr: 1.0000e-04 Epoch 39/2000 900/900 [==============================] - 2s 2ms/step - loss: 1.8850e-04 - val_loss: 9.9578e-05 - lr: 1.0000e-04 Epoch 40/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.8244e-04 - val_loss: 1.0522e-04 - lr: 1.0000e-04 Epoch 41/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3757e-04 - val_loss: 1.5331e-04 - lr: 1.0000e-04 Epoch 42/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3224e-04 - val_loss: 2.4568e-04 - lr: 1.0000e-04 Epoch 43/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.6857e-04 - val_loss: 1.4375e-04 - lr: 1.0000e-04 Epoch 44/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3927e-04 - val_loss: 3.8073e-04 - lr: 1.0000e-04 Epoch 45/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.6187e-04 - val_loss: 4.2486e-04 - lr: 1.0000e-04 Epoch 46/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.4784e-04 - val_loss: 1.7491e-04 - lr: 1.0000e-04 Epoch 47/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.5885e-04 - val_loss: 1.2637e-04 - lr: 1.0000e-04 Epoch 48/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3876e-04 - val_loss: 9.0454e-05 - lr: 1.0000e-04 Epoch 49/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.7796e-04 - val_loss: 1.3724e-04 - lr: 1.0000e-04 Epoch 50/2000 900/900 [==============================] - 2s 2ms/step - loss: 1.3802e-04 - val_loss: 1.1495e-04 - lr: 1.0000e-04 Epoch 51/2000 900/900 [==============================] - 2s 2ms/step - loss: 1.4784e-04 - val_loss: 1.0661e-04 - lr: 1.0000e-04 Epoch 52/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2565e-04 - val_loss: 9.0812e-05 - lr: 1.0000e-04 Epoch 53/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.4147e-04 - val_loss: 1.0544e-04 - lr: 1.0000e-04 Epoch 54/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.4119e-04 - val_loss: 5.1870e-04 - lr: 1.0000e-04 Epoch 55/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.4186e-04 - val_loss: 7.9401e-05 - lr: 1.0000e-04 Epoch 56/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.7324e-04 - val_loss: 9.3971e-05 - lr: 1.0000e-04 Epoch 57/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3775e-04 - val_loss: 1.4554e-04 - lr: 1.0000e-04 Epoch 58/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2992e-04 - val_loss: 9.5643e-05 - lr: 1.0000e-04 Epoch 59/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2934e-04 - val_loss: 7.1712e-05 - lr: 1.0000e-04 Epoch 60/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3317e-04 - val_loss: 1.5182e-04 - lr: 1.0000e-04 Epoch 61/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2192e-04 - val_loss: 9.4130e-05 - lr: 1.0000e-04 Epoch 62/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2367e-04 - val_loss: 1.1338e-04 - lr: 1.0000e-04 Epoch 63/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.5802e-04 - val_loss: 1.1068e-04 - lr: 1.0000e-04 Epoch 64/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1099e-04 - val_loss: 1.8395e-04 - lr: 1.0000e-04 Epoch 65/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2799e-04 - val_loss: 6.3500e-05 - lr: 1.0000e-04 Epoch 66/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2981e-04 - val_loss: 1.4402e-04 - lr: 1.0000e-04 Epoch 67/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2969e-04 - val_loss: 6.7762e-05 - lr: 1.0000e-04 Epoch 68/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3877e-04 - val_loss: 9.6731e-05 - lr: 1.0000e-04 Epoch 69/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1277e-04 - val_loss: 1.3771e-04 - lr: 1.0000e-04 Epoch 70/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1472e-04 - val_loss: 1.2268e-04 - lr: 1.0000e-04 Epoch 71/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1190e-04 - val_loss: 7.2661e-05 - lr: 1.0000e-04 Epoch 72/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3607e-04 - val_loss: 1.3418e-04 - lr: 1.0000e-04 Epoch 73/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1247e-04 - val_loss: 2.3557e-04 - lr: 1.0000e-04 Epoch 74/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1410e-04 - val_loss: 9.0923e-05 - lr: 1.0000e-04 Epoch 75/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1888e-04 - val_loss: 2.2146e-04 - lr: 1.0000e-04
fig, ax = plt.subplots(figsize=(10, 7))
ax.plot(history.history['loss'], label='Training Loss')
ax.plot(history.history['val_loss'], label='Validation Loss')
ax.set(
title='Processo de otimização das funções de perda',
ylabel='Loss',
xlabel='Epoch'
)
plt.legend()
plt.tight_layout()
plt.show()
predictions = mlp.predict(x_test)
inverse_predictions = scaler.inverse_transform(predictions)
63/63 [==============================] - 0s 996us/step
fig, ax = plt.subplots(figsize=(15, 9), subplot_kw=dict(projection='3d'))
ax.plot_wireframe(x1, x2, y, linewidths=0.5, color='lightgrey')
ax.scatter(x_test[:,0], x_test[:,1], scaler.inverse_transform(y_test), s=14, color='C0', label='Training data')
ax.scatter(x_test[:,0], x_test[:,1], inverse_predictions, s=15, marker='^', color='C1', label='Test data')
ax.set(
xlabel='$x_1$',
ylabel='$x_2$',
zlabel='$f(x_1, x_2)$'
)
plt.legend()
plt.tight_layout()
plt.show()
mse = mean_squared_error(scaler.inverse_transform(y_test), inverse_predictions)
rmse = mean_squared_error(scaler.inverse_transform(y_test), inverse_predictions, squared=False)
mae = mean_absolute_error(scaler.inverse_transform(y_test), inverse_predictions)
print(f"Mean Squared Error: {mse}")
print(f"Root Mean Squared Error: {rmse}")
print(f"Mean Absolute Error: {mae}")
Mean Squared Error: 16880097.554985106 Root Mean Squared Error: 4108.5395890736045 Mean Absolute Error: 2477.902080862183
$x_1^2 + x_2^2 + 2x_1x_2cos(\pi x_1x_2) + x_1 + x_2 -1$ com $|x_1| ≤1 , |x_2| ≤ 1$
# function's definition
def g(x1,x2):
return x1**2 + x2**2 + 2 * x1 * x2 * np.cos(np.pi * x1 * x2) + x1 + x2 - 1
# generating points
x1, x2 = np.meshgrid(np.linspace(-1, 1, 100), np.linspace(-1, 1, 100))
y = g(x1,x2)
# plotting surface
fig, ax = plt.subplots(figsize=(10, 7), subplot_kw=dict(projection='3d'))
ax.plot_surface(x1, x2, y)
ax.set(
xlabel='$x_1$',
ylabel='$x_2$',
zlabel='$f(x_1, x_2)$'
)
plt.tight_layout()
plt.show()
# split train test
x_train, x_test, y_train, y_test = train_test_split(
np.vstack([x1.flatten(), x2.flatten()]).T,
y.flatten(),
test_size=0.2,
random_state=505
)
# surface os points to test and to train
fig, ax = plt.subplots(figsize=(10, 7), subplot_kw=dict(projection='3d'))
ax.plot_wireframe(x1, x2, y, linewidths=0.5, color='lightgrey')
ax.scatter(x_train[:,0], x_train[:,1], y_train, s=1, color='darkorange', label='Training data')
ax.scatter(x_test[:,0], x_test[:,1], y_test, s=5, color='darkgreen', label='Test data')
ax.set(
xlabel='$x_1$',
ylabel='$x_2$',
zlabel='$f(x_1, x_2)$'
)
plt.legend()
plt.tight_layout()
plt.show()
mlp = Sequential([
Dense(64, activation='relu', input_shape=(2,)),
Dense(32, activation='relu'),
Dense(16, activation='relu'),
Dense(8, activation='relu'),
Dense(4, activation='relu'),
Dense(1, activation='linear')
])
mlp.compile(
loss='mean_squared_error',
optimizer='adam'
)
mlp.summary()
Model: "sequential_3"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
dense_18 (Dense) (None, 64) 192
dense_19 (Dense) (None, 32) 2080
dense_20 (Dense) (None, 16) 528
dense_21 (Dense) (None, 8) 136
dense_22 (Dense) (None, 4) 36
dense_23 (Dense) (None, 1) 5
=================================================================
Total params: 2,977
Trainable params: 2,977
Non-trainable params: 0
_________________________________________________________________
# training the model
history = mlp.fit(
x_train, y_train,
batch_size=8,
epochs=2000,
validation_split=0.1,
callbacks=[
tf.keras.callbacks.EarlyStopping(monitor='val_loss', patience=10),
tf.keras.callbacks.ReduceLROnPlateau(monitor='val_loss', factor=0.1, patience=5, min_lr=0.0001)
]
)
Epoch 1/2000 900/900 [==============================] - 2s 1ms/step - loss: 0.3755 - val_loss: 0.1831 - lr: 0.0010 Epoch 2/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.1221 - val_loss: 0.0754 - lr: 0.0010 Epoch 3/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0488 - val_loss: 0.0392 - lr: 0.0010 Epoch 4/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0238 - val_loss: 0.0227 - lr: 0.0010 Epoch 5/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0188 - val_loss: 0.0208 - lr: 0.0010 Epoch 6/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0147 - val_loss: 0.0175 - lr: 0.0010 Epoch 7/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0147 - val_loss: 0.0202 - lr: 0.0010 Epoch 8/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0169 - val_loss: 0.0165 - lr: 0.0010 Epoch 9/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0135 - val_loss: 0.0165 - lr: 0.0010 Epoch 10/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0148 - val_loss: 0.0140 - lr: 0.0010 Epoch 11/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0100 - val_loss: 0.0106 - lr: 0.0010 Epoch 12/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0096 - val_loss: 0.0085 - lr: 0.0010 Epoch 13/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0058 - val_loss: 0.0064 - lr: 0.0010 Epoch 14/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0059 - val_loss: 0.0047 - lr: 0.0010 Epoch 15/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0049 - val_loss: 0.0043 - lr: 0.0010 Epoch 16/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0033 - val_loss: 0.0029 - lr: 0.0010 Epoch 17/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0027 - val_loss: 0.0028 - lr: 0.0010 Epoch 18/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0024 - val_loss: 0.0037 - lr: 0.0010 Epoch 19/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0030 - val_loss: 0.0022 - lr: 0.0010 Epoch 20/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0035 - val_loss: 0.0016 - lr: 0.0010 Epoch 21/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0013 - val_loss: 0.0039 - lr: 0.0010 Epoch 22/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0017 - val_loss: 0.0012 - lr: 0.0010 Epoch 23/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0017 - val_loss: 0.0011 - lr: 0.0010 Epoch 24/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0017 - val_loss: 0.0026 - lr: 0.0010 Epoch 25/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0010 - val_loss: 0.0046 - lr: 0.0010 Epoch 26/2000 900/900 [==============================] - 2s 2ms/step - loss: 0.0016 - val_loss: 8.2744e-04 - lr: 0.0010 Epoch 27/2000 900/900 [==============================] - 2s 2ms/step - loss: 0.0014 - val_loss: 0.0011 - lr: 0.0010 Epoch 28/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0018 - val_loss: 7.3059e-04 - lr: 0.0010 Epoch 29/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0013 - val_loss: 0.0021 - lr: 0.0010 Epoch 30/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0013 - val_loss: 5.2872e-04 - lr: 0.0010 Epoch 31/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.0995e-04 - val_loss: 7.3022e-04 - lr: 0.0010 Epoch 32/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0019 - val_loss: 0.0014 - lr: 0.0010 Epoch 33/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.4458e-04 - val_loss: 9.2240e-04 - lr: 0.0010 Epoch 34/2000 900/900 [==============================] - 1s 1ms/step - loss: 0.0019 - val_loss: 7.6538e-04 - lr: 0.0010 Epoch 35/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.7375e-04 - val_loss: 5.7007e-04 - lr: 0.0010 Epoch 36/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.5156e-04 - val_loss: 3.2450e-04 - lr: 1.0000e-04 Epoch 37/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.4211e-04 - val_loss: 3.0920e-04 - lr: 1.0000e-04 Epoch 38/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3987e-04 - val_loss: 3.2047e-04 - lr: 1.0000e-04 Epoch 39/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.4100e-04 - val_loss: 2.8895e-04 - lr: 1.0000e-04 Epoch 40/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3653e-04 - val_loss: 3.0373e-04 - lr: 1.0000e-04 Epoch 41/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3535e-04 - val_loss: 2.6592e-04 - lr: 1.0000e-04 Epoch 42/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3654e-04 - val_loss: 2.6799e-04 - lr: 1.0000e-04 Epoch 43/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.3816e-04 - val_loss: 2.5570e-04 - lr: 1.0000e-04 Epoch 44/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2641e-04 - val_loss: 2.9339e-04 - lr: 1.0000e-04 Epoch 45/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2121e-04 - val_loss: 3.2909e-04 - lr: 1.0000e-04 Epoch 46/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.2684e-04 - val_loss: 2.3325e-04 - lr: 1.0000e-04 Epoch 47/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1775e-04 - val_loss: 2.6653e-04 - lr: 1.0000e-04 Epoch 48/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1174e-04 - val_loss: 2.3168e-04 - lr: 1.0000e-04 Epoch 49/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1471e-04 - val_loss: 2.5295e-04 - lr: 1.0000e-04 Epoch 50/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.1344e-04 - val_loss: 2.6298e-04 - lr: 1.0000e-04 Epoch 51/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.0876e-04 - val_loss: 2.0776e-04 - lr: 1.0000e-04 Epoch 52/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.0718e-04 - val_loss: 2.1121e-04 - lr: 1.0000e-04 Epoch 53/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.0307e-04 - val_loss: 2.0588e-04 - lr: 1.0000e-04 Epoch 54/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.0388e-04 - val_loss: 1.9177e-04 - lr: 1.0000e-04 Epoch 55/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.0178e-04 - val_loss: 2.0274e-04 - lr: 1.0000e-04 Epoch 56/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.0178e-04 - val_loss: 2.2856e-04 - lr: 1.0000e-04 Epoch 57/2000 900/900 [==============================] - 1s 1ms/step - loss: 1.0126e-04 - val_loss: 2.3026e-04 - lr: 1.0000e-04 Epoch 58/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.3505e-05 - val_loss: 2.0378e-04 - lr: 1.0000e-04 Epoch 59/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.6313e-05 - val_loss: 1.8932e-04 - lr: 1.0000e-04 Epoch 60/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.1047e-05 - val_loss: 1.8083e-04 - lr: 1.0000e-04 Epoch 61/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.8763e-05 - val_loss: 1.8094e-04 - lr: 1.0000e-04 Epoch 62/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.1101e-05 - val_loss: 1.8211e-04 - lr: 1.0000e-04 Epoch 63/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.0412e-05 - val_loss: 1.9709e-04 - lr: 1.0000e-04 Epoch 64/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.3721e-05 - val_loss: 2.6898e-04 - lr: 1.0000e-04 Epoch 65/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.3494e-05 - val_loss: 1.8946e-04 - lr: 1.0000e-04 Epoch 66/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.1262e-05 - val_loss: 1.7357e-04 - lr: 1.0000e-04 Epoch 67/2000 900/900 [==============================] - 1s 1ms/step - loss: 8.6589e-05 - val_loss: 1.6051e-04 - lr: 1.0000e-04 Epoch 68/2000 900/900 [==============================] - 1s 1ms/step - loss: 8.8745e-05 - val_loss: 1.6204e-04 - lr: 1.0000e-04 Epoch 69/2000 900/900 [==============================] - 1s 1ms/step - loss: 8.2716e-05 - val_loss: 1.5193e-04 - lr: 1.0000e-04 Epoch 70/2000 900/900 [==============================] - 1s 1ms/step - loss: 8.5516e-05 - val_loss: 1.4889e-04 - lr: 1.0000e-04 Epoch 71/2000 900/900 [==============================] - 1s 1ms/step - loss: 8.7297e-05 - val_loss: 1.4578e-04 - lr: 1.0000e-04 Epoch 72/2000 900/900 [==============================] - 1s 1ms/step - loss: 8.0910e-05 - val_loss: 1.4944e-04 - lr: 1.0000e-04 Epoch 73/2000 900/900 [==============================] - 1s 1ms/step - loss: 8.8776e-05 - val_loss: 1.7773e-04 - lr: 1.0000e-04 Epoch 74/2000 900/900 [==============================] - 1s 1ms/step - loss: 8.2522e-05 - val_loss: 1.4596e-04 - lr: 1.0000e-04 Epoch 75/2000 900/900 [==============================] - 1s 1ms/step - loss: 8.4255e-05 - val_loss: 1.3306e-04 - lr: 1.0000e-04 Epoch 76/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.8852e-05 - val_loss: 1.6480e-04 - lr: 1.0000e-04 Epoch 77/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.2539e-05 - val_loss: 1.3074e-04 - lr: 1.0000e-04 Epoch 78/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.7328e-05 - val_loss: 1.2497e-04 - lr: 1.0000e-04 Epoch 79/2000 900/900 [==============================] - 1s 1ms/step - loss: 9.1113e-05 - val_loss: 1.4063e-04 - lr: 1.0000e-04 Epoch 80/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.1518e-05 - val_loss: 1.1932e-04 - lr: 1.0000e-04 Epoch 81/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.8567e-05 - val_loss: 1.3577e-04 - lr: 1.0000e-04 Epoch 82/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.6544e-05 - val_loss: 1.2487e-04 - lr: 1.0000e-04 Epoch 83/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.4925e-05 - val_loss: 1.4861e-04 - lr: 1.0000e-04 Epoch 84/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.4571e-05 - val_loss: 1.4264e-04 - lr: 1.0000e-04 Epoch 85/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.9797e-05 - val_loss: 1.1468e-04 - lr: 1.0000e-04 Epoch 86/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.4416e-05 - val_loss: 1.3066e-04 - lr: 1.0000e-04 Epoch 87/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.3910e-05 - val_loss: 1.5394e-04 - lr: 1.0000e-04 Epoch 88/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.9360e-05 - val_loss: 1.1626e-04 - lr: 1.0000e-04 Epoch 89/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.7308e-05 - val_loss: 1.1188e-04 - lr: 1.0000e-04 Epoch 90/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.2721e-05 - val_loss: 1.1300e-04 - lr: 1.0000e-04 Epoch 91/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.7185e-05 - val_loss: 1.2724e-04 - lr: 1.0000e-04 Epoch 92/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.7134e-05 - val_loss: 1.1569e-04 - lr: 1.0000e-04 Epoch 93/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.8117e-05 - val_loss: 1.1088e-04 - lr: 1.0000e-04 Epoch 94/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.8846e-05 - val_loss: 1.3633e-04 - lr: 1.0000e-04 Epoch 95/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.7340e-05 - val_loss: 1.2110e-04 - lr: 1.0000e-04 Epoch 96/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.7974e-05 - val_loss: 1.7295e-04 - lr: 1.0000e-04 Epoch 97/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.7266e-05 - val_loss: 1.1850e-04 - lr: 1.0000e-04 Epoch 98/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.2741e-05 - val_loss: 1.2930e-04 - lr: 1.0000e-04 Epoch 99/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.4239e-05 - val_loss: 1.0425e-04 - lr: 1.0000e-04 Epoch 100/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.8227e-05 - val_loss: 1.0128e-04 - lr: 1.0000e-04 Epoch 101/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.1065e-05 - val_loss: 1.0580e-04 - lr: 1.0000e-04 Epoch 102/2000 900/900 [==============================] - 1s 1ms/step - loss: 7.2595e-05 - val_loss: 1.0268e-04 - lr: 1.0000e-04 Epoch 103/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.0114e-05 - val_loss: 1.3312e-04 - lr: 1.0000e-04 Epoch 104/2000 900/900 [==============================] - 1s 2ms/step - loss: 6.9939e-05 - val_loss: 1.1080e-04 - lr: 1.0000e-04 Epoch 105/2000 900/900 [==============================] - 2s 2ms/step - loss: 6.1671e-05 - val_loss: 9.3537e-05 - lr: 1.0000e-04 Epoch 106/2000 900/900 [==============================] - 2s 2ms/step - loss: 6.9090e-05 - val_loss: 1.0073e-04 - lr: 1.0000e-04 Epoch 107/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.0073e-05 - val_loss: 1.4321e-04 - lr: 1.0000e-04 Epoch 108/2000 900/900 [==============================] - 1s 1ms/step - loss: 5.8665e-05 - val_loss: 1.0323e-04 - lr: 1.0000e-04 Epoch 109/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.1377e-05 - val_loss: 2.0407e-04 - lr: 1.0000e-04 Epoch 110/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.5973e-05 - val_loss: 9.2555e-05 - lr: 1.0000e-04 Epoch 111/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.1832e-05 - val_loss: 1.1252e-04 - lr: 1.0000e-04 Epoch 112/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.1293e-05 - val_loss: 8.5153e-05 - lr: 1.0000e-04 Epoch 113/2000 900/900 [==============================] - 1s 1ms/step - loss: 5.6221e-05 - val_loss: 9.7618e-05 - lr: 1.0000e-04 Epoch 114/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.3836e-05 - val_loss: 9.4311e-05 - lr: 1.0000e-04 Epoch 115/2000 900/900 [==============================] - 1s 1ms/step - loss: 5.8413e-05 - val_loss: 1.3108e-04 - lr: 1.0000e-04 Epoch 116/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.1561e-05 - val_loss: 9.7013e-05 - lr: 1.0000e-04 Epoch 117/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.2772e-05 - val_loss: 1.0615e-04 - lr: 1.0000e-04 Epoch 118/2000 900/900 [==============================] - 1s 1ms/step - loss: 5.7437e-05 - val_loss: 1.3355e-04 - lr: 1.0000e-04 Epoch 119/2000 900/900 [==============================] - 1s 1ms/step - loss: 5.7079e-05 - val_loss: 9.6611e-05 - lr: 1.0000e-04 Epoch 120/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.2548e-05 - val_loss: 1.0475e-04 - lr: 1.0000e-04 Epoch 121/2000 900/900 [==============================] - 1s 1ms/step - loss: 5.7250e-05 - val_loss: 1.1300e-04 - lr: 1.0000e-04 Epoch 122/2000 900/900 [==============================] - 1s 1ms/step - loss: 6.4314e-05 - val_loss: 9.1217e-05 - lr: 1.0000e-04
# plotting loss function
fig, ax = plt.subplots(figsize=(10, 7))
ax.plot(history.history['loss'], label='Training Loss')
ax.plot(history.history['val_loss'], label='Validation Loss')
ax.set(
title='Processo de otimização das funções de perda',
ylabel='Loss',
xlabel='Epoch'
)
plt.legend()
plt.tight_layout()
plt.show()
# true points and predicted points
fig, ax = plt.subplots(figsize=(15, 9), subplot_kw=dict(projection='3d'))
ax.plot_wireframe(x1, x2, y, linewidths=0.5, color='lightgrey')
ax.scatter(x_test[:,0], x_test[:,1], y_test, s=14, color='C0', label='Training data')
ax.scatter(x_test[:,0], x_test[:,1], mlp.predict(x_test), s=15, marker='^', color='C1', label='Test data')
ax.set(
xlabel='$x_1$',
ylabel='$x_2$',
zlabel='$f(x_1, x_2)$'
)
plt.legend()
plt.tight_layout()
plt.show()
63/63 [==============================] - 0s 1ms/step
mse = mean_squared_error(y_test, mlp.predict(x_test))
rmse = mean_squared_error(y_test, mlp.predict(x_test), squared=False)
mae = mean_absolute_error(y_test, mlp.predict(x_test))
63/63 [==============================] - 0s 903us/step 63/63 [==============================] - 0s 988us/step 63/63 [==============================] - 0s 763us/step
print(f"Mean Squared Error: {mse}")
print(f"Root Mean Squared Error: {rmse}")
print(f"Mean Absolute Error: {mae}")
Mean Squared Error: 4.9327674554969855e-05 Root Mean Squared Error: 0.007023366326411421 Mean Absolute Error: 0.0053168037015980385
Considere o problema de classificação de padrões bidimensionais constituído neste caso de 5 padrões. A distribuição dos padrões tem como base um quadrado centrado na origem interceptando os eixos nos pontos +1 e -1 de cada eixo. Os pontos +1 e -1 de cada eixo são centros de quatro semicírculos que se interceptam no interior do quadrado originando as classes 1,2,3,4 e a outra classe corresponde as regiões de não interseção. Após gerar aleato- riamente os dados que venham formar estas distribuições de dados, selecione um conjunto de treinamento e um conjunto de validação com o rótulo de cada classe. Solucione este problema considerando uma rede perceptron de múltiplas camada. Apresente na solução a curva do erro médio de treinamento e a curva do erro médio de teste. Apresente também a matriz de confusão.
# Semicírculo azul
def c1(x, y):
if (x + 1)**2 + y**2 <= 1:
return 1
else:
return 0
#Sermicírculo verde
def c2(x, y):
if (x - 1)**2 + y**2 <= 1:
return 1
else:
return 0
#Semicírculo amarelo
def c3(x, y):
if x**2 + (y + 1)**2 <= 1:
return 1
else:
return 0
#Semicírculo vermelha=o
def c4(x, y):
if x**2 + (y - 1)**2 <= 1:
return 1
else:
return 0
x, y = np.meshgrid(np.linspace(-1, 1, 100), np.linspace(-1, 1, 100))
points = np.vstack(list(zip(x.ravel(), y.ravel())))
lista = []
for x_i, y_i in points:
if c1(x_i, y_i) + c4(x_i, y_i) == 2:
lista.append(1)
elif c2(x_i, y_i) + c4(x_i, y_i) == 2:
lista.append(2)
elif c2(x_i, y_i) + c3(x_i, y_i) == 2:
lista.append(3)
elif c1(x_i, y_i) + c3(x_i, y_i) == 2:
lista.append(4)
else:
lista.append(0)
labels = np.array(lista)
x_train, x_test, y_train, y_test = train_test_split(points, labels, test_size=0.2, stratify=labels)
print(f"shape x train: {x_train.shape}")
print(f"shape y train: {y_train.shape}")
print(f"shape x test: {x_test.shape}")
print(f"shape y test: {y_test.shape}")
shape x train: (8000, 2) shape y train: (8000,) shape x test: (2000, 2) shape y test: (2000,)
fig, ax = plt.subplots(ncols=3, figsize=(40, 12))
color1 = (181/255, 181/255, 181/255, 1.0)
color2 = (38/255, 118/255, 222/255, 1.0)
color3 = (38/255, 222/255, 118/255, 1.0)
color4 = (235/255, 91/255, 156/255, 1.0)
color5 = (240/255, 130/255, 44/255, 1.0)
colormap = np.array([color1, color2, color3, color4, color5])
dataset_scatter = ax[0].scatter(points[:,0], points[:,1], c=colormap[labels], marker='d')
ax[0].set(
title='Dataset',
xlabel='$x$',
ylabel='$y$'
)
ax[1].scatter(x_train[:,0], x_train[:,1], c=colormap[y_train], marker='d')
ax[1].set(
title='Training set',
xlabel='$x$',
ylabel='$y$'
)
ax[2].scatter(x_test[:,0], x_test[:,1], c=colormap[y_test], marker='d')
ax[2].set(
title='Test set',
xlabel='$x$',
ylabel='$y$'
)
from matplotlib.patches import Patch
from matplotlib.lines import Line2D
legend_elements = [
Line2D([0], [0], marker='o', color='w', label='Scatter', markerfacecolor=(181/255, 181/255, 181/255), markersize=15),
Line2D([0], [0], marker='o', color='w', label='Scatter', markerfacecolor=(38/255, 118/255, 222/255), markersize=15),
Line2D([0], [0], marker='o', color='w', label='Scatter', markerfacecolor=(38/255, 222/255, 118/255), markersize=15),
Line2D([0], [0], marker='o', color='w', label='Scatter', markerfacecolor=(235/255, 91/255, 156/255), markersize=15),
Line2D([0], [0], marker='o', color='w', label='Scatter', markerfacecolor=(240/255, 130/255, 44/255), markersize=15)
]
fig.legend(
legend_elements,
['0', '1', '2', '3', '4'],
loc='lower center',
title='Classes'
)
plt.show()
mlp = Sequential([
Dense(64, activation='relu', input_shape=(2,)),
Dense(32, activation='relu'),
Dense(16, activation='relu'),
Dense(8, activation='relu'),
Dense(5, activation='softmax')
])
mlp.compile(
loss='sparse_categorical_crossentropy',
optimizer='adam',
metrics=['acc']
)
mlp.summary()
Model: "sequential_1"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
dense_5 (Dense) (None, 64) 192
dense_6 (Dense) (None, 32) 2080
dense_7 (Dense) (None, 16) 528
dense_8 (Dense) (None, 8) 136
dense_9 (Dense) (None, 5) 45
=================================================================
Total params: 2,981
Trainable params: 2,981
Non-trainable params: 0
_________________________________________________________________
history = mlp.fit(
x_train, y_train.reshape((-1,1)),
validation_split=0.1,
batch_size=10,
epochs=2000,
callbacks=[
tf.keras.callbacks.EarlyStopping(monitor='loss', patience=10),
tf.keras.callbacks.ReduceLROnPlateau(monitor='loss', factor=0.1, patience=5, min_lr=0.0001)
]
)
Epoch 1/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.7271 - acc: 0.6861 - val_loss: 0.4313 - val_acc: 0.8350 - lr: 0.0010 Epoch 2/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.3175 - acc: 0.8826 - val_loss: 0.2762 - val_acc: 0.8975 - lr: 0.0010 Epoch 3/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.2327 - acc: 0.9156 - val_loss: 0.2305 - val_acc: 0.9125 - lr: 0.0010 Epoch 4/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.1948 - acc: 0.9292 - val_loss: 0.1951 - val_acc: 0.9162 - lr: 0.0010 Epoch 5/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1680 - acc: 0.9410 - val_loss: 0.1584 - val_acc: 0.9438 - lr: 0.0010 Epoch 6/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1588 - acc: 0.9375 - val_loss: 0.1548 - val_acc: 0.9375 - lr: 0.0010 Epoch 7/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1468 - acc: 0.9440 - val_loss: 0.1422 - val_acc: 0.9438 - lr: 0.0010 Epoch 8/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1337 - acc: 0.9468 - val_loss: 0.1154 - val_acc: 0.9550 - lr: 0.0010 Epoch 9/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1251 - acc: 0.9507 - val_loss: 0.1369 - val_acc: 0.9350 - lr: 0.0010 Epoch 10/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1272 - acc: 0.9499 - val_loss: 0.1201 - val_acc: 0.9575 - lr: 0.0010 Epoch 11/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1169 - acc: 0.9533 - val_loss: 0.1246 - val_acc: 0.9438 - lr: 0.0010 Epoch 12/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1170 - acc: 0.9517 - val_loss: 0.1711 - val_acc: 0.9212 - lr: 0.0010 Epoch 13/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1165 - acc: 0.9532 - val_loss: 0.1301 - val_acc: 0.9438 - lr: 0.0010 Epoch 14/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1164 - acc: 0.9524 - val_loss: 0.0993 - val_acc: 0.9588 - lr: 0.0010 Epoch 15/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1120 - acc: 0.9519 - val_loss: 0.1097 - val_acc: 0.9488 - lr: 0.0010 Epoch 16/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1062 - acc: 0.9569 - val_loss: 0.1492 - val_acc: 0.9337 - lr: 0.0010 Epoch 17/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1104 - acc: 0.9533 - val_loss: 0.0911 - val_acc: 0.9588 - lr: 0.0010 Epoch 18/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1109 - acc: 0.9550 - val_loss: 0.1208 - val_acc: 0.9525 - lr: 0.0010 Epoch 19/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1010 - acc: 0.9592 - val_loss: 0.1122 - val_acc: 0.9513 - lr: 0.0010 Epoch 20/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0980 - acc: 0.9599 - val_loss: 0.0863 - val_acc: 0.9638 - lr: 0.0010 Epoch 21/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0965 - acc: 0.9596 - val_loss: 0.0889 - val_acc: 0.9613 - lr: 0.0010 Epoch 22/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0994 - acc: 0.9597 - val_loss: 0.1672 - val_acc: 0.9262 - lr: 0.0010 Epoch 23/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0979 - acc: 0.9589 - val_loss: 0.1394 - val_acc: 0.9463 - lr: 0.0010 Epoch 24/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1035 - acc: 0.9558 - val_loss: 0.0798 - val_acc: 0.9638 - lr: 0.0010 Epoch 25/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0924 - acc: 0.9633 - val_loss: 0.0743 - val_acc: 0.9688 - lr: 0.0010 Epoch 26/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0937 - acc: 0.9601 - val_loss: 0.1888 - val_acc: 0.9425 - lr: 0.0010 Epoch 27/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.1012 - acc: 0.9583 - val_loss: 0.0916 - val_acc: 0.9600 - lr: 0.0010 Epoch 28/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0925 - acc: 0.9617 - val_loss: 0.0768 - val_acc: 0.9613 - lr: 0.0010 Epoch 29/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0933 - acc: 0.9632 - val_loss: 0.1094 - val_acc: 0.9513 - lr: 0.0010 Epoch 30/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0930 - acc: 0.9617 - val_loss: 0.0828 - val_acc: 0.9613 - lr: 0.0010 Epoch 31/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0574 - acc: 0.9829 - val_loss: 0.0603 - val_acc: 0.9737 - lr: 1.0000e-04 Epoch 32/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0554 - acc: 0.9847 - val_loss: 0.0665 - val_acc: 0.9712 - lr: 1.0000e-04 Epoch 33/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0549 - acc: 0.9856 - val_loss: 0.0587 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 34/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0556 - acc: 0.9844 - val_loss: 0.0582 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 35/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0544 - acc: 0.9847 - val_loss: 0.0599 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 36/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0542 - acc: 0.9847 - val_loss: 0.0614 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 37/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0544 - acc: 0.9851 - val_loss: 0.0634 - val_acc: 0.9737 - lr: 1.0000e-04 Epoch 38/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0536 - acc: 0.9846 - val_loss: 0.0570 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 39/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0530 - acc: 0.9854 - val_loss: 0.0511 - val_acc: 0.9837 - lr: 1.0000e-04 Epoch 40/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0536 - acc: 0.9858 - val_loss: 0.0554 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 41/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0527 - acc: 0.9862 - val_loss: 0.0612 - val_acc: 0.9737 - lr: 1.0000e-04 Epoch 42/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0527 - acc: 0.9856 - val_loss: 0.0540 - val_acc: 0.9837 - lr: 1.0000e-04 Epoch 43/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0519 - acc: 0.9861 - val_loss: 0.0597 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 44/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0513 - acc: 0.9869 - val_loss: 0.0547 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 45/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0514 - acc: 0.9861 - val_loss: 0.0577 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 46/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0511 - acc: 0.9850 - val_loss: 0.0548 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 47/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0518 - acc: 0.9847 - val_loss: 0.0580 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 48/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0509 - acc: 0.9861 - val_loss: 0.0565 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 49/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0502 - acc: 0.9868 - val_loss: 0.0508 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 50/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0505 - acc: 0.9854 - val_loss: 0.0611 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 51/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0492 - acc: 0.9862 - val_loss: 0.0535 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 52/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0493 - acc: 0.9858 - val_loss: 0.0552 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 53/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0495 - acc: 0.9868 - val_loss: 0.0559 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 54/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0487 - acc: 0.9856 - val_loss: 0.0526 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 55/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0490 - acc: 0.9867 - val_loss: 0.0565 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 56/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0484 - acc: 0.9864 - val_loss: 0.0520 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 57/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0481 - acc: 0.9882 - val_loss: 0.0494 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 58/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0476 - acc: 0.9882 - val_loss: 0.0550 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 59/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0478 - acc: 0.9872 - val_loss: 0.0577 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 60/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0480 - acc: 0.9864 - val_loss: 0.0521 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 61/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0476 - acc: 0.9872 - val_loss: 0.0478 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 62/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0477 - acc: 0.9865 - val_loss: 0.0485 - val_acc: 0.9812 - lr: 1.0000e-04 Epoch 63/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0471 - acc: 0.9857 - val_loss: 0.0510 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 64/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0464 - acc: 0.9890 - val_loss: 0.0604 - val_acc: 0.9737 - lr: 1.0000e-04 Epoch 65/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0470 - acc: 0.9878 - val_loss: 0.0538 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 66/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0463 - acc: 0.9878 - val_loss: 0.0523 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 67/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0462 - acc: 0.9868 - val_loss: 0.0496 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 68/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0458 - acc: 0.9871 - val_loss: 0.0516 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 69/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0458 - acc: 0.9875 - val_loss: 0.0488 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 70/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0460 - acc: 0.9871 - val_loss: 0.0504 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 71/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0462 - acc: 0.9868 - val_loss: 0.0586 - val_acc: 0.9725 - lr: 1.0000e-04 Epoch 72/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0450 - acc: 0.9879 - val_loss: 0.0515 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 73/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0450 - acc: 0.9882 - val_loss: 0.0560 - val_acc: 0.9725 - lr: 1.0000e-04 Epoch 74/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0450 - acc: 0.9890 - val_loss: 0.0512 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 75/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0452 - acc: 0.9881 - val_loss: 0.0480 - val_acc: 0.9812 - lr: 1.0000e-04 Epoch 76/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0441 - acc: 0.9889 - val_loss: 0.0443 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 77/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0446 - acc: 0.9868 - val_loss: 0.0481 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 78/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0442 - acc: 0.9876 - val_loss: 0.0562 - val_acc: 0.9737 - lr: 1.0000e-04 Epoch 79/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0439 - acc: 0.9885 - val_loss: 0.0434 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 80/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0443 - acc: 0.9867 - val_loss: 0.0488 - val_acc: 0.9812 - lr: 1.0000e-04 Epoch 81/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0437 - acc: 0.9893 - val_loss: 0.0470 - val_acc: 0.9812 - lr: 1.0000e-04 Epoch 82/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0436 - acc: 0.9885 - val_loss: 0.0456 - val_acc: 0.9875 - lr: 1.0000e-04 Epoch 83/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0432 - acc: 0.9885 - val_loss: 0.0515 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 84/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0443 - acc: 0.9871 - val_loss: 0.0486 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 85/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0431 - acc: 0.9886 - val_loss: 0.0446 - val_acc: 0.9875 - lr: 1.0000e-04 Epoch 86/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0430 - acc: 0.9886 - val_loss: 0.0506 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 87/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0430 - acc: 0.9886 - val_loss: 0.0503 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 88/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0430 - acc: 0.9890 - val_loss: 0.0529 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 89/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0423 - acc: 0.9887 - val_loss: 0.0550 - val_acc: 0.9712 - lr: 1.0000e-04 Epoch 90/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0426 - acc: 0.9889 - val_loss: 0.0499 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 91/2000 720/720 [==============================] - 3s 4ms/step - loss: 0.0415 - acc: 0.9906 - val_loss: 0.0428 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 92/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0422 - acc: 0.9882 - val_loss: 0.0472 - val_acc: 0.9837 - lr: 1.0000e-04 Epoch 93/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0422 - acc: 0.9883 - val_loss: 0.0434 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 94/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0425 - acc: 0.9883 - val_loss: 0.0464 - val_acc: 0.9837 - lr: 1.0000e-04 Epoch 95/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0415 - acc: 0.9903 - val_loss: 0.0567 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 96/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0416 - acc: 0.9903 - val_loss: 0.0423 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 97/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0418 - acc: 0.9889 - val_loss: 0.0464 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 98/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0410 - acc: 0.9906 - val_loss: 0.0502 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 99/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0414 - acc: 0.9896 - val_loss: 0.0430 - val_acc: 0.9887 - lr: 1.0000e-04 Epoch 100/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0408 - acc: 0.9894 - val_loss: 0.0437 - val_acc: 0.9875 - lr: 1.0000e-04 Epoch 101/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0413 - acc: 0.9885 - val_loss: 0.0478 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 102/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0408 - acc: 0.9893 - val_loss: 0.0418 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 103/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0403 - acc: 0.9896 - val_loss: 0.0454 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 104/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0406 - acc: 0.9881 - val_loss: 0.0420 - val_acc: 0.9887 - lr: 1.0000e-04 Epoch 105/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0410 - acc: 0.9883 - val_loss: 0.0502 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 106/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0410 - acc: 0.9889 - val_loss: 0.0394 - val_acc: 0.9900 - lr: 1.0000e-04 Epoch 107/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0401 - acc: 0.9887 - val_loss: 0.0515 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 108/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0400 - acc: 0.9900 - val_loss: 0.0409 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 109/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0405 - acc: 0.9892 - val_loss: 0.0411 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 110/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0407 - acc: 0.9879 - val_loss: 0.0589 - val_acc: 0.9688 - lr: 1.0000e-04 Epoch 111/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0392 - acc: 0.9896 - val_loss: 0.0581 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 112/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0394 - acc: 0.9896 - val_loss: 0.0492 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 113/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0395 - acc: 0.9890 - val_loss: 0.0449 - val_acc: 0.9837 - lr: 1.0000e-04 Epoch 114/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0396 - acc: 0.9878 - val_loss: 0.0389 - val_acc: 0.9875 - lr: 1.0000e-04 Epoch 115/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0393 - acc: 0.9901 - val_loss: 0.0464 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 116/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0395 - acc: 0.9893 - val_loss: 0.0502 - val_acc: 0.9725 - lr: 1.0000e-04 Epoch 117/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0390 - acc: 0.9885 - val_loss: 0.0448 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 118/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0385 - acc: 0.9899 - val_loss: 0.0396 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 119/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0391 - acc: 0.9900 - val_loss: 0.0409 - val_acc: 0.9837 - lr: 1.0000e-04 Epoch 120/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0386 - acc: 0.9914 - val_loss: 0.0514 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 121/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0392 - acc: 0.9889 - val_loss: 0.0431 - val_acc: 0.9812 - lr: 1.0000e-04 Epoch 122/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0389 - acc: 0.9894 - val_loss: 0.0447 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 123/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0382 - acc: 0.9894 - val_loss: 0.0507 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 124/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0384 - acc: 0.9899 - val_loss: 0.0406 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 125/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0378 - acc: 0.9901 - val_loss: 0.0470 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 126/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0384 - acc: 0.9889 - val_loss: 0.0460 - val_acc: 0.9812 - lr: 1.0000e-04 Epoch 127/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0383 - acc: 0.9889 - val_loss: 0.0390 - val_acc: 0.9887 - lr: 1.0000e-04 Epoch 128/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0381 - acc: 0.9875 - val_loss: 0.0396 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 129/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0381 - acc: 0.9894 - val_loss: 0.0554 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 130/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0378 - acc: 0.9889 - val_loss: 0.0478 - val_acc: 0.9725 - lr: 1.0000e-04 Epoch 131/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0373 - acc: 0.9903 - val_loss: 0.0416 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 132/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0383 - acc: 0.9893 - val_loss: 0.0394 - val_acc: 0.9900 - lr: 1.0000e-04 Epoch 133/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0372 - acc: 0.9899 - val_loss: 0.0383 - val_acc: 0.9900 - lr: 1.0000e-04 Epoch 134/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0373 - acc: 0.9901 - val_loss: 0.0469 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 135/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0371 - acc: 0.9897 - val_loss: 0.0401 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 136/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0377 - acc: 0.9890 - val_loss: 0.0436 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 137/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0368 - acc: 0.9894 - val_loss: 0.0405 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 138/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0363 - acc: 0.9897 - val_loss: 0.0450 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 139/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0371 - acc: 0.9900 - val_loss: 0.0392 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 140/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0370 - acc: 0.9899 - val_loss: 0.0474 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 141/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0363 - acc: 0.9892 - val_loss: 0.0386 - val_acc: 0.9812 - lr: 1.0000e-04 Epoch 142/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0371 - acc: 0.9889 - val_loss: 0.0436 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 143/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0365 - acc: 0.9908 - val_loss: 0.0487 - val_acc: 0.9737 - lr: 1.0000e-04 Epoch 144/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0366 - acc: 0.9892 - val_loss: 0.0380 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 145/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0363 - acc: 0.9900 - val_loss: 0.0393 - val_acc: 0.9837 - lr: 1.0000e-04 Epoch 146/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0371 - acc: 0.9899 - val_loss: 0.0374 - val_acc: 0.9887 - lr: 1.0000e-04 Epoch 147/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0362 - acc: 0.9894 - val_loss: 0.0489 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 148/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0359 - acc: 0.9894 - val_loss: 0.0459 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 149/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0360 - acc: 0.9899 - val_loss: 0.0328 - val_acc: 0.9937 - lr: 1.0000e-04 Epoch 150/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0357 - acc: 0.9892 - val_loss: 0.0459 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 151/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0351 - acc: 0.9896 - val_loss: 0.0425 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 152/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0365 - acc: 0.9885 - val_loss: 0.0402 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 153/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0350 - acc: 0.9906 - val_loss: 0.0390 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 154/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0362 - acc: 0.9894 - val_loss: 0.0378 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 155/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0365 - acc: 0.9878 - val_loss: 0.0366 - val_acc: 0.9900 - lr: 1.0000e-04 Epoch 156/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0352 - acc: 0.9907 - val_loss: 0.0386 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 157/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0351 - acc: 0.9897 - val_loss: 0.0435 - val_acc: 0.9762 - lr: 1.0000e-04 Epoch 158/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0350 - acc: 0.9910 - val_loss: 0.0530 - val_acc: 0.9700 - lr: 1.0000e-04 Epoch 159/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0345 - acc: 0.9904 - val_loss: 0.0379 - val_acc: 0.9812 - lr: 1.0000e-04 Epoch 160/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0359 - acc: 0.9886 - val_loss: 0.0375 - val_acc: 0.9887 - lr: 1.0000e-04 Epoch 161/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0347 - acc: 0.9906 - val_loss: 0.0394 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 162/2000 720/720 [==============================] - 3s 4ms/step - loss: 0.0345 - acc: 0.9900 - val_loss: 0.0400 - val_acc: 0.9875 - lr: 1.0000e-04 Epoch 163/2000 720/720 [==============================] - 3s 4ms/step - loss: 0.0346 - acc: 0.9907 - val_loss: 0.0372 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 164/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0348 - acc: 0.9892 - val_loss: 0.0340 - val_acc: 0.9925 - lr: 1.0000e-04 Epoch 165/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0346 - acc: 0.9897 - val_loss: 0.0386 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 166/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0356 - acc: 0.9887 - val_loss: 0.0398 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 167/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0347 - acc: 0.9904 - val_loss: 0.0436 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 168/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0345 - acc: 0.9897 - val_loss: 0.0350 - val_acc: 0.9875 - lr: 1.0000e-04 Epoch 169/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0333 - acc: 0.9899 - val_loss: 0.0433 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 170/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0345 - acc: 0.9890 - val_loss: 0.0370 - val_acc: 0.9837 - lr: 1.0000e-04 Epoch 171/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0343 - acc: 0.9897 - val_loss: 0.0417 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 172/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0342 - acc: 0.9896 - val_loss: 0.0353 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 173/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0348 - acc: 0.9904 - val_loss: 0.0407 - val_acc: 0.9812 - lr: 1.0000e-04 Epoch 174/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0334 - acc: 0.9912 - val_loss: 0.0405 - val_acc: 0.9812 - lr: 1.0000e-04 Epoch 175/2000 720/720 [==============================] - 3s 4ms/step - loss: 0.0338 - acc: 0.9912 - val_loss: 0.0392 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 176/2000 720/720 [==============================] - 4s 6ms/step - loss: 0.0341 - acc: 0.9892 - val_loss: 0.0326 - val_acc: 0.9887 - lr: 1.0000e-04 Epoch 177/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0339 - acc: 0.9907 - val_loss: 0.0433 - val_acc: 0.9775 - lr: 1.0000e-04 Epoch 178/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0328 - acc: 0.9896 - val_loss: 0.0374 - val_acc: 0.9850 - lr: 1.0000e-04 Epoch 179/2000 720/720 [==============================] - 5s 8ms/step - loss: 0.0339 - acc: 0.9889 - val_loss: 0.0330 - val_acc: 0.9887 - lr: 1.0000e-04 Epoch 180/2000 720/720 [==============================] - 3s 4ms/step - loss: 0.0330 - acc: 0.9907 - val_loss: 0.0345 - val_acc: 0.9912 - lr: 1.0000e-04 Epoch 181/2000 720/720 [==============================] - 4s 6ms/step - loss: 0.0335 - acc: 0.9903 - val_loss: 0.0344 - val_acc: 0.9887 - lr: 1.0000e-04 Epoch 182/2000 720/720 [==============================] - 4s 5ms/step - loss: 0.0325 - acc: 0.9915 - val_loss: 0.0348 - val_acc: 0.9875 - lr: 1.0000e-04 Epoch 183/2000 720/720 [==============================] - 2s 3ms/step - loss: 0.0334 - acc: 0.9904 - val_loss: 0.0411 - val_acc: 0.9787 - lr: 1.0000e-04 Epoch 184/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0336 - acc: 0.9906 - val_loss: 0.0375 - val_acc: 0.9837 - lr: 1.0000e-04 Epoch 185/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0334 - acc: 0.9903 - val_loss: 0.0397 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 186/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0329 - acc: 0.9907 - val_loss: 0.0452 - val_acc: 0.9750 - lr: 1.0000e-04 Epoch 187/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0334 - acc: 0.9908 - val_loss: 0.0334 - val_acc: 0.9862 - lr: 1.0000e-04 Epoch 188/2000 720/720 [==============================] - 3s 5ms/step - loss: 0.0332 - acc: 0.9906 - val_loss: 0.0378 - val_acc: 0.9825 - lr: 1.0000e-04 Epoch 189/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0329 - acc: 0.9904 - val_loss: 0.0425 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 190/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0328 - acc: 0.9901 - val_loss: 0.0316 - val_acc: 0.9912 - lr: 1.0000e-04 Epoch 191/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0330 - acc: 0.9911 - val_loss: 0.0463 - val_acc: 0.9800 - lr: 1.0000e-04 Epoch 192/2000 720/720 [==============================] - 2s 2ms/step - loss: 0.0326 - acc: 0.9908 - val_loss: 0.0391 - val_acc: 0.9825 - lr: 1.0000e-04
fig, ax = plt.subplots(ncols=2, figsize=(16, 6))
ax[0].plot(history.history['loss'], label='Training loss')
ax[0].plot(history.history['val_loss'], label='Validation loss')
ax[0].legend()
ax[0].set(
ylabel='Loss',
xlabel='Epoch'
)
ax[1].plot(history.history['acc'], label='Training accuracy')
ax[1].plot(history.history['val_acc'], label='Validation accuracy')
ax[1].set(
ylabel='Accuracy',
xlabel='Epoch'
)
plt.legend()
plt.tight_layout()
plt.show()
predictions = [np.argmax(p) for p in mlp.predict(x_test)]
63/63 [==============================] - 0s 1ms/step
print(classification_report(y_test, predictions))
precision recall f1-score support
0 0.99 0.98 0.98 884
1 0.98 0.99 0.98 279
2 1.00 0.98 0.99 279
3 0.98 1.00 0.99 279
4 0.99 1.00 0.99 279
accuracy 0.99 2000
macro avg 0.99 0.99 0.99 2000
weighted avg 0.99 0.99 0.99 2000
fig, ax = plt.subplots(figsize=(14, 8))
ConfusionMatrixDisplay(confusion_matrix(predictions, y_test)).plot(values_format='.0f', ax=ax)
ax.set(
title='Confusion Matrix',
xlabel='True Labels',
ylabel='Predicted Labels'
)
plt.tight_layout()
plt.show()
fig, ax = plt.subplots(figsize=(12, 12))
ax.scatter(x_test[:,0], x_test[:,1], c=y_test, marker='d')
ax.scatter(x_test[:,0], x_test[:,1], c=predictions, marker='x')
ax.set(
title='Predictions',
xlabel='$x$',
ylabel='$y$'
)
plt.show()
Considere uma rede deep learning convolutiva (treinada) aplicada à classificação de padrões em imagens. A base de dados considerada é a CIFAR-10 (pesquise). A referida base de dados consiste de 60 mil imagens coloridas de 32x32 pixels, com 50 mil para treino e 10 mil para teste. As imagens estão divididas em 10 classes, a saber: avião, navio, cami- nhão, automóvel, sapo, pássaro, cachorro, gato, cavalo e cervo. Cada imagem possui apenas um dos objetos da classe de interesse, podendo estar parcialmente obstruído por outros ob- jetos que não pertençam a esse conjunto. Apresente os resultados da classificação em uma matriz de confusão.
Este trabalho foi baseado no trabalho do CODERONIN1 do Kaggle Link: https://www.kaggle.com/code/adi160/cifar-10-keras-transfer-learning
from sklearn.utils.multiclass import unique_labels
import os
import matplotlib.image as mpimg
import seaborn as sns
from keras.layers import Flatten,Dense,BatchNormalization,Activation,Dropout
from keras.utils import to_categorical
from tensorflow.keras.callbacks import EarlyStopping
# library for transfer learning
from keras.applications import VGG19,ResNet50
# data augumentation
from keras.preprocessing.image import ImageDataGenerator
# import dataset
from keras.datasets import cifar10
# load dataset and divide in train and teste datasets
(x_train, y_train), (x_test, y_test) = cifar10.load_data()
print(f"shape x train: {x_train.shape}")
print(f"shape y train: {y_train.shape}")
print(f"shape x test: {x_test.shape}")
print(f"shape y test: {y_test.shape}")
shape x train: (50000, 32, 32, 3) shape y train: (50000, 1) shape x test: (10000, 32, 32, 3) shape y test: (10000, 1)
y_train=to_categorical(y_train)
y_test=to_categorical(y_test)
print(f"shape x train: {x_train.shape}")
print(f"shape y train: {y_train.shape}")
print(f"shape x test: {x_test.shape}")
print(f"shape y test: {y_test.shape}")
shape x train: (50000, 32, 32, 3) shape y train: (50000, 10) shape x test: (10000, 32, 32, 3) shape y test: (10000, 10)
# Let's instantiate the object
train_generator = ImageDataGenerator(
rotation_range=2,
horizontal_flip=True,
zoom_range=.1 )
test_generator = ImageDataGenerator(
rotation_range=2,
horizontal_flip= True,
zoom_range=.1)
#Fit the augmentation method to the data
train_generator.fit(x_train)
test_generator.fit(x_test)
lrr= ReduceLROnPlateau(
monitor='val_accuracy', #Metric to be measured
factor=.01, #Factor by which learning rate will be reduced
patience=3, #No. of epochs after which if there is no improvement in the val_acc, the learning rate is reduced
min_lr=1e-5) #The minimum learning rate
# The first base model used is VGG19.
# The pretrained weights from the imagenet challenge are used
base_vgg19 = VGG19(include_top=False,
input_shape=(32,32,3),
classes=y_train.shape[1],
weights='imagenet')
base_vgg19.summary()
Model: "vgg19"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
input_4 (InputLayer) [(None, 32, 32, 3)] 0
block1_conv1 (Conv2D) (None, 32, 32, 64) 1792
block1_conv2 (Conv2D) (None, 32, 32, 64) 36928
block1_pool (MaxPooling2D) (None, 16, 16, 64) 0
block2_conv1 (Conv2D) (None, 16, 16, 128) 73856
block2_conv2 (Conv2D) (None, 16, 16, 128) 147584
block2_pool (MaxPooling2D) (None, 8, 8, 128) 0
block3_conv1 (Conv2D) (None, 8, 8, 256) 295168
block3_conv2 (Conv2D) (None, 8, 8, 256) 590080
block3_conv3 (Conv2D) (None, 8, 8, 256) 590080
block3_conv4 (Conv2D) (None, 8, 8, 256) 590080
block3_pool (MaxPooling2D) (None, 4, 4, 256) 0
block4_conv1 (Conv2D) (None, 4, 4, 512) 1180160
block4_conv2 (Conv2D) (None, 4, 4, 512) 2359808
block4_conv3 (Conv2D) (None, 4, 4, 512) 2359808
block4_conv4 (Conv2D) (None, 4, 4, 512) 2359808
block4_pool (MaxPooling2D) (None, 2, 2, 512) 0
block5_conv1 (Conv2D) (None, 2, 2, 512) 2359808
block5_conv2 (Conv2D) (None, 2, 2, 512) 2359808
block5_conv3 (Conv2D) (None, 2, 2, 512) 2359808
block5_conv4 (Conv2D) (None, 2, 2, 512) 2359808
block5_pool (MaxPooling2D) (None, 1, 1, 512) 0
=================================================================
Total params: 20,024,384
Trainable params: 20,024,384
Non-trainable params: 0
_________________________________________________________________
vgg19 = Sequential()
vgg19.add(base_vgg19)
vgg19.add(Flatten())
#Add the Dense layers along with activation and batch normalization
vgg19.add(Dense(1024,activation=('relu'),input_dim=512))
vgg19.add(Dense(512,activation=('relu')))
vgg19.add(Dense(256,activation=('relu')))
#model_1.add(Dropout(.3))
vgg19.add(Dense(128,activation=('relu')))
#model_1.add(Dropout(.2))
vgg19.add(Dense(10,activation=('softmax')))
vgg19.summary()
Model: "sequential_3"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
vgg19 (Functional) (None, 1, 1, 512) 20024384
flatten_3 (Flatten) (None, 512) 0
dense_15 (Dense) (None, 1024) 525312
dense_16 (Dense) (None, 512) 524800
dense_17 (Dense) (None, 256) 131328
dense_18 (Dense) (None, 128) 32896
dense_19 (Dense) (None, 10) 1290
=================================================================
Total params: 21,240,010
Trainable params: 21,240,010
Non-trainable params: 0
_________________________________________________________________
# hyperparameters
batch_size= 100
epochs=50
learn_rate=.001
sgd=SGD(lr=learn_rate,momentum=.9,nesterov=False)
adam=Adam(lr=learn_rate, beta_1=0.9, beta_2=0.999,
epsilon=None, decay=0.0, amsgrad=False)
vgg19.compile(optimizer=sgd,
loss='categorical_crossentropy',
metrics=['accuracy'])
vgg19.fit_generator(train_generator.flow(x_train,y_train,batch_size=batch_size),
epochs=epochs,
steps_per_epoch=x_train.shape[0]//batch_size,
validation_data=test_generator.flow(x_test,y_test,batch_size=batch_size),validation_steps=250,
callbacks=[lrr],verbose=1)
Epoch 1/50
/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:5: UserWarning: `Model.fit_generator` is deprecated and will be removed in a future version. Please use `Model.fit`, which supports generators. """
500/500 [==============================] - ETA: 0s - loss: 1.6137 - accuracy: 0.4008
WARNING:tensorflow:Your input ran out of data; interrupting training. Make sure that your dataset or generator can generate at least `steps_per_epoch * epochs` batches (in this case, 250 batches). You may need to use the repeat() function when building your dataset.
500/500 [==============================] - 37s 73ms/step - loss: 1.6137 - accuracy: 0.4008 - val_loss: 1.0790 - val_accuracy: 0.6240 - lr: 0.0010 Epoch 2/50 500/500 [==============================] - ETA: 0s - loss: 0.8359 - accuracy: 0.7123
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.8359 - accuracy: 0.7123 - lr: 0.0010 Epoch 3/50 500/500 [==============================] - ETA: 0s - loss: 0.6465 - accuracy: 0.7799
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 33s 65ms/step - loss: 0.6465 - accuracy: 0.7799 - lr: 0.0010 Epoch 4/50 500/500 [==============================] - ETA: 0s - loss: 0.5492 - accuracy: 0.8131
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.5492 - accuracy: 0.8131 - lr: 0.0010 Epoch 5/50 500/500 [==============================] - ETA: 0s - loss: 0.4832 - accuracy: 0.8365
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.4832 - accuracy: 0.8365 - lr: 0.0010 Epoch 6/50 500/500 [==============================] - ETA: 0s - loss: 0.4242 - accuracy: 0.8548
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.4242 - accuracy: 0.8548 - lr: 0.0010 Epoch 7/50 500/500 [==============================] - ETA: 0s - loss: 0.3861 - accuracy: 0.8667
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.3861 - accuracy: 0.8667 - lr: 0.0010 Epoch 8/50 500/500 [==============================] - ETA: 0s - loss: 0.3509 - accuracy: 0.8775
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 35s 70ms/step - loss: 0.3509 - accuracy: 0.8775 - lr: 0.0010 Epoch 9/50 500/500 [==============================] - ETA: 0s - loss: 0.3144 - accuracy: 0.8912
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.3144 - accuracy: 0.8912 - lr: 0.0010 Epoch 10/50 500/500 [==============================] - ETA: 0s - loss: 0.2832 - accuracy: 0.9022
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.2832 - accuracy: 0.9022 - lr: 0.0010 Epoch 11/50 500/500 [==============================] - ETA: 0s - loss: 0.2564 - accuracy: 0.9116
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.2564 - accuracy: 0.9116 - lr: 0.0010 Epoch 12/50 500/500 [==============================] - ETA: 0s - loss: 0.2257 - accuracy: 0.9214
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.2257 - accuracy: 0.9214 - lr: 0.0010 Epoch 13/50 500/500 [==============================] - ETA: 0s - loss: 0.2134 - accuracy: 0.9262
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.2134 - accuracy: 0.9262 - lr: 0.0010 Epoch 14/50 500/500 [==============================] - ETA: 0s - loss: 0.1928 - accuracy: 0.9343
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.1928 - accuracy: 0.9343 - lr: 0.0010 Epoch 15/50 500/500 [==============================] - ETA: 0s - loss: 0.1731 - accuracy: 0.9400
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.1731 - accuracy: 0.9400 - lr: 0.0010 Epoch 16/50 500/500 [==============================] - ETA: 0s - loss: 0.1550 - accuracy: 0.9474
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.1550 - accuracy: 0.9474 - lr: 0.0010 Epoch 17/50 500/500 [==============================] - ETA: 0s - loss: 0.1412 - accuracy: 0.9514
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.1412 - accuracy: 0.9514 - lr: 0.0010 Epoch 18/50 500/500 [==============================] - ETA: 0s - loss: 0.1307 - accuracy: 0.9560
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.1307 - accuracy: 0.9560 - lr: 0.0010 Epoch 19/50 500/500 [==============================] - ETA: 0s - loss: 0.1171 - accuracy: 0.9605
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.1171 - accuracy: 0.9605 - lr: 0.0010 Epoch 20/50 500/500 [==============================] - ETA: 0s - loss: 0.1071 - accuracy: 0.9633
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.1071 - accuracy: 0.9633 - lr: 0.0010 Epoch 21/50 500/500 [==============================] - ETA: 0s - loss: 0.1004 - accuracy: 0.9654
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.1004 - accuracy: 0.9654 - lr: 0.0010 Epoch 22/50 500/500 [==============================] - ETA: 0s - loss: 0.0919 - accuracy: 0.9687
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0919 - accuracy: 0.9687 - lr: 0.0010 Epoch 23/50 500/500 [==============================] - ETA: 0s - loss: 0.0862 - accuracy: 0.9704
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 34s 68ms/step - loss: 0.0862 - accuracy: 0.9704 - lr: 0.0010 Epoch 24/50 500/500 [==============================] - ETA: 0s - loss: 0.0761 - accuracy: 0.9743
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0761 - accuracy: 0.9743 - lr: 0.0010 Epoch 25/50 500/500 [==============================] - ETA: 0s - loss: 0.0703 - accuracy: 0.9761
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0703 - accuracy: 0.9761 - lr: 0.0010 Epoch 26/50 500/500 [==============================] - ETA: 0s - loss: 0.0664 - accuracy: 0.9768
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0664 - accuracy: 0.9768 - lr: 0.0010 Epoch 27/50 500/500 [==============================] - ETA: 0s - loss: 0.0601 - accuracy: 0.9798
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0601 - accuracy: 0.9798 - lr: 0.0010 Epoch 28/50 500/500 [==============================] - ETA: 0s - loss: 0.0578 - accuracy: 0.9802
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0578 - accuracy: 0.9802 - lr: 0.0010 Epoch 29/50 500/500 [==============================] - ETA: 0s - loss: 0.0568 - accuracy: 0.9805
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0568 - accuracy: 0.9805 - lr: 0.0010 Epoch 30/50 500/500 [==============================] - ETA: 0s - loss: 0.0488 - accuracy: 0.9842
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0488 - accuracy: 0.9842 - lr: 0.0010 Epoch 31/50 500/500 [==============================] - ETA: 0s - loss: 0.0475 - accuracy: 0.9842
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0475 - accuracy: 0.9842 - lr: 0.0010 Epoch 32/50 500/500 [==============================] - ETA: 0s - loss: 0.0455 - accuracy: 0.9844
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0455 - accuracy: 0.9844 - lr: 0.0010 Epoch 33/50 500/500 [==============================] - ETA: 0s - loss: 0.0433 - accuracy: 0.9855
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0433 - accuracy: 0.9855 - lr: 0.0010 Epoch 34/50 500/500 [==============================] - ETA: 0s - loss: 0.0404 - accuracy: 0.9866
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0404 - accuracy: 0.9866 - lr: 0.0010 Epoch 35/50 500/500 [==============================] - ETA: 0s - loss: 0.0433 - accuracy: 0.9849
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0433 - accuracy: 0.9849 - lr: 0.0010 Epoch 36/50 500/500 [==============================] - ETA: 0s - loss: 0.0367 - accuracy: 0.9876
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0367 - accuracy: 0.9876 - lr: 0.0010 Epoch 37/50 500/500 [==============================] - ETA: 0s - loss: 0.0306 - accuracy: 0.9895
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0306 - accuracy: 0.9895 - lr: 0.0010 Epoch 38/50 500/500 [==============================] - ETA: 0s - loss: 0.0300 - accuracy: 0.9896
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0300 - accuracy: 0.9896 - lr: 0.0010 Epoch 39/50 500/500 [==============================] - ETA: 0s - loss: 0.0328 - accuracy: 0.9892
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0328 - accuracy: 0.9892 - lr: 0.0010 Epoch 40/50 500/500 [==============================] - ETA: 0s - loss: 0.0263 - accuracy: 0.9912
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0263 - accuracy: 0.9912 - lr: 0.0010 Epoch 41/50 500/500 [==============================] - ETA: 0s - loss: 0.0276 - accuracy: 0.9909
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0276 - accuracy: 0.9909 - lr: 0.0010 Epoch 42/50 500/500 [==============================] - ETA: 0s - loss: 0.0274 - accuracy: 0.9908
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 33s 65ms/step - loss: 0.0274 - accuracy: 0.9908 - lr: 0.0010 Epoch 43/50 500/500 [==============================] - ETA: 0s - loss: 0.0267 - accuracy: 0.9907
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0267 - accuracy: 0.9907 - lr: 0.0010 Epoch 44/50 500/500 [==============================] - ETA: 0s - loss: 0.0308 - accuracy: 0.9895
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0308 - accuracy: 0.9895 - lr: 0.0010 Epoch 45/50 500/500 [==============================] - ETA: 0s - loss: 0.0257 - accuracy: 0.9914
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0257 - accuracy: 0.9914 - lr: 0.0010 Epoch 46/50 500/500 [==============================] - ETA: 0s - loss: 0.0220 - accuracy: 0.9930
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0220 - accuracy: 0.9930 - lr: 0.0010 Epoch 47/50 500/500 [==============================] - ETA: 0s - loss: 0.0216 - accuracy: 0.9928
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 65ms/step - loss: 0.0216 - accuracy: 0.9928 - lr: 0.0010 Epoch 48/50 500/500 [==============================] - ETA: 0s - loss: 0.0211 - accuracy: 0.9928
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0211 - accuracy: 0.9928 - lr: 0.0010 Epoch 49/50 500/500 [==============================] - ETA: 0s - loss: 0.0216 - accuracy: 0.9926
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 33s 65ms/step - loss: 0.0216 - accuracy: 0.9926 - lr: 0.0010 Epoch 50/50 500/500 [==============================] - ETA: 0s - loss: 0.0230 - accuracy: 0.9920
WARNING:tensorflow:Learning rate reduction is conditioned on metric `val_accuracy` which is not available. Available metrics are: loss,accuracy,lr
500/500 [==============================] - 32s 64ms/step - loss: 0.0230 - accuracy: 0.9920 - lr: 0.0010
<keras.callbacks.History at 0x7f660232e310>
fig, ax = plt.subplots(ncols=2, figsize=(16, 6))
ax[0].plot(vgg19.history.history['loss'], label='Training loss')
ax[0].plot(vgg19.history.history['val_loss'], label='Validation loss')
ax[0].legend()
ax[0].set(
ylabel='Loss',
xlabel='Epoch'
)
ax[1].plot(vgg19.history.history['accuracy'], label='Training accuracy')
ax[1].plot(vgg19.history.history['val_accuracy'], label='Validation accuracy')
ax[1].set(
ylabel='Accuracy',
xlabel='Epoch'
)
plt.legend()
plt.tight_layout()
plt.show()
def plot_confusion_matrix(y_true, y_pred, classes,
normalize=False,
title=None,
cmap=plt.cm.Blues):
"""
This function prints and plots the confusion matrix.
Normalization can be applied by setting `normalize=True`.
"""
if not title:
if normalize:
title = 'Normalized confusion matrix'
else:
title = 'Confusion matrix, without normalization'
# Compute confusion matrix
cm = confusion_matrix(y_true, y_pred)
if normalize:
cm = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]
print("Normalized confusion matrix")
else:
print('Confusion matrix, without normalization')
# print(cm)
fig, ax = plt.subplots(figsize=(7,7))
im = ax.imshow(cm, interpolation='nearest', cmap=cmap)
ax.figure.colorbar(im, ax=ax)
# We want to show all ticks...
ax.set(xticks=np.arange(cm.shape[1]),
yticks=np.arange(cm.shape[0]),
# ... and label them with the respective list entries
xticklabels=classes, yticklabels=classes,
title=title,
ylabel='True label',
xlabel='Predicted label')
# Rotate the tick labels and set their alignment.
plt.setp(ax.get_xticklabels(), rotation=45, ha="right",
rotation_mode="anchor")
# Loop over data dimensions and create text annotations.
fmt = '.2f' if normalize else 'd'
thresh = cm.max() / 2.
for i in range(cm.shape[0]):
for j in range(cm.shape[1]):
ax.text(j, i, format(cm[i, j], fmt),
ha="center", va="center",
color="white" if cm[i, j] > thresh else "black")
fig.tight_layout()
return ax
np.set_printoptions(precision=2)
y_pred = vgg19.predict(x_test)
y_pred = np.argmax(y_pred,axis=1)
y_true=np.argmax(y_test,axis=1)
#Compute the confusion matrix
confusion_mtx = confusion_matrix(y_true,y_pred)
313/313 [==============================] - 4s 10ms/step
class_names=['airplane', 'automobile', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']
# Plot non-normalized confusion matrix
plot_confusion_matrix(y_true, y_pred, classes=class_names,
title='Confusion matrix, without normalization')
Confusion matrix, without normalization
<matplotlib.axes._subplots.AxesSubplot at 0x7f64c4167a10>
# Plot normalized confusion matrix
plot_confusion_matrix(y_true, y_pred, classes=class_names, normalize=True,
title='Normalized confusion matrix')
# plt.show()
Normalized confusion matrix
<matplotlib.axes._subplots.AxesSubplot at 0x7f64ba2477d0>
print(classification_report(y_true, y_pred, target_names=class_names))
precision recall f1-score support
airplane 0.89 0.89 0.89 1000
automobile 0.91 0.95 0.93 1000
bird 0.90 0.80 0.85 1000
cat 0.77 0.70 0.74 1000
deer 0.86 0.87 0.86 1000
dog 0.78 0.82 0.80 1000
frog 0.89 0.90 0.90 1000
horse 0.89 0.90 0.89 1000
ship 0.93 0.93 0.93 1000
truck 0.87 0.94 0.90 1000
accuracy 0.87 10000
macro avg 0.87 0.87 0.87 10000
weighted avg 0.87 0.87 0.87 10000
Utilize a rede neural perceptron de múltiplas camadas do tipo NARX (rede recorrente) para fazer a predição de um passo $x^{(n+1)}$ da série temporal $x(n) = 1 + cos(n + cos^2(n))$, n=0,1,2,3,.... Gere inicialmente um conjunto de amostras para o treinamento, definindo o erro de predição como $e^{(n+1)}=x(n+1)-x^{(n+1)}$. Avalie o desempenho mostrando a curva a série temporal, a curva de predição o e curva do erro de predição.
from tensorflow.keras.layers import Dense, Reshape, Flatten, Dropout, Activation, BatchNormalization, LSTM, Embedding, Input
from tensorflow.keras.preprocessing.sequence import TimeseriesGenerator
from tensorflow.keras.callbacks import EarlyStopping, ReduceLROnPlateau
# defining function
def f(x):
return 1 + np.cos(x + (np.cos(x))**2)
x = np.linspace(0, 100, 10000)
y = [f(i) for i in x]
# plot data
points = 10000
plt.plot(x[:points], y[:points])
plt.show()
# splitting data into training and testing
test_size = 2000
x_train = x[:-test_size]
y_train = y[:-test_size]
x_test = x[-test_size:]
y_test = y[-test_size:]
# plot data
fig, axes = plt.subplots(ncols=1, figsize=(24, 5))
axes.plot(x_train, y_train, label='train')
axes.plot(x_test, y_test, label='test')
axes.set_title('Data')
axes.legend()
plt.show()
sequence_x = list(TimeseriesGenerator(x_train, x_train, 4, batch_size=1))
sequence_y = list(TimeseriesGenerator(x_train[4:], x_train[4:], 3, batch_size=1))
train_seqs = []
y_train = []
for (x_seq, next_x), (next_seq, _) in zip(sequence_x, sequence_y):
seq = np.append(x_seq.reshape(4,), next_seq.reshape(3, ))
train_seqs.append(seq)
y_train.append(next_x)
train_seqs = np.array(train_seqs)
y_train = np.array(y_train)
sequence_x = list(TimeseriesGenerator(x_test, x_test, 4, batch_size=1))
sequence_y = list(TimeseriesGenerator(x_test[4:], x_test[4:], 3, batch_size=1))
test_seqs = []
y_test = []
for (x_seq, next_x), (next_seq, _) in zip(sequence_x, sequence_y):
seq = np.append(x_seq.reshape(4,), next_seq.reshape(3, ))
test_seqs.append(seq)
y_test.append(next_x)
test_seqs = np.array(test_seqs)
y_test = np.array(y_test)
# building the model
model = Sequential([
LSTM(128, input_shape=(7, 1), return_sequences=True),
LSTM(64, return_sequences=True),
LSTM(32),
Dense(1)
])
model.compile(loss="mean_absolute_error", optimizer="rmsprop")
model.summary()
Model: "sequential_3"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
lstm_9 (LSTM) (None, 7, 128) 66560
lstm_10 (LSTM) (None, 7, 64) 49408
lstm_11 (LSTM) (None, 32) 12416
dense_3 (Dense) (None, 1) 33
=================================================================
Total params: 128,417
Trainable params: 128,417
Non-trainable params: 0
_________________________________________________________________
# Training the model
history = model.fit(
train_seqs, y_train,
validation_split=0.1,
batch_size=8,
epochs=350,
shuffle=True,
callbacks=[
EarlyStopping(monitor='val_loss', patience=5),
ReduceLROnPlateau(monitor='val_loss', factor=0.1, patience=5, min_lr=0.0001)
]
)
Epoch 1/350 900/900 [==============================] - 15s 13ms/step - loss: 19.2268 - val_loss: 42.0530 - lr: 0.0010 Epoch 2/350 900/900 [==============================] - 10s 11ms/step - loss: 5.9539 - val_loss: 21.8673 - lr: 0.0010 Epoch 3/350 900/900 [==============================] - 10s 11ms/step - loss: 1.8953 - val_loss: 11.9836 - lr: 0.0010 Epoch 4/350 900/900 [==============================] - 12s 13ms/step - loss: 1.0453 - val_loss: 7.9481 - lr: 0.0010 Epoch 5/350 900/900 [==============================] - 11s 12ms/step - loss: 0.8444 - val_loss: 6.3535 - lr: 0.0010 Epoch 6/350 900/900 [==============================] - 10s 11ms/step - loss: 0.7501 - val_loss: 5.6213 - lr: 0.0010 Epoch 7/350 900/900 [==============================] - 9s 10ms/step - loss: 0.6863 - val_loss: 5.3713 - lr: 0.0010 Epoch 8/350 900/900 [==============================] - 12s 13ms/step - loss: 0.6383 - val_loss: 5.0735 - lr: 0.0010 Epoch 9/350 900/900 [==============================] - 11s 12ms/step - loss: 0.6063 - val_loss: 4.9584 - lr: 0.0010 Epoch 10/350 900/900 [==============================] - 9s 10ms/step - loss: 0.5673 - val_loss: 5.5064 - lr: 0.0010 Epoch 11/350 900/900 [==============================] - 9s 10ms/step - loss: 0.5476 - val_loss: 4.8842 - lr: 0.0010 Epoch 12/350 900/900 [==============================] - 9s 10ms/step - loss: 0.5189 - val_loss: 4.8164 - lr: 0.0010 Epoch 13/350 900/900 [==============================] - 10s 11ms/step - loss: 0.5060 - val_loss: 4.5964 - lr: 0.0010 Epoch 14/350 900/900 [==============================] - 9s 10ms/step - loss: 0.4958 - val_loss: 4.4385 - lr: 0.0010 Epoch 15/350 900/900 [==============================] - 10s 11ms/step - loss: 0.4765 - val_loss: 4.3941 - lr: 0.0010 Epoch 16/350 900/900 [==============================] - 9s 10ms/step - loss: 0.4595 - val_loss: 4.3836 - lr: 0.0010 Epoch 17/350 900/900 [==============================] - 9s 10ms/step - loss: 0.4499 - val_loss: 4.6375 - lr: 0.0010 Epoch 18/350 900/900 [==============================] - 9s 10ms/step - loss: 0.4343 - val_loss: 4.1039 - lr: 0.0010 Epoch 19/350 900/900 [==============================] - 10s 11ms/step - loss: 0.4234 - val_loss: 4.4430 - lr: 0.0010 Epoch 20/350 900/900 [==============================] - 14s 15ms/step - loss: 0.4182 - val_loss: 4.1976 - lr: 0.0010 Epoch 21/350 900/900 [==============================] - 12s 13ms/step - loss: 0.4104 - val_loss: 4.3439 - lr: 0.0010 Epoch 22/350 900/900 [==============================] - 12s 14ms/step - loss: 0.3992 - val_loss: 4.3010 - lr: 0.0010 Epoch 23/350 900/900 [==============================] - 12s 14ms/step - loss: 0.3901 - val_loss: 4.5941 - lr: 0.0010
# plotting loss
fig, ax = plt.subplots(figsize=(8, 6))
ax.plot(history.history['loss'], label='Training loss')
ax.plot(history.history['val_loss'], label='Validation loss')
ax.legend()
ax.set(
ylabel='Loss',
xlabel='Epoch'
)
plt.legend()
plt.tight_layout()
plt.show()
# predicting
y_pred = model.predict(test_seqs)
63/63 [==============================] - 1s 5ms/step
erro = y_test - y_pred
fig, ax = plt.subplots(figsize=(12, 6))
ax.bar(
x=range(len(erro)),
height=erro.flatten()
)
ax.set(
title='Erro da Predição',
ylabel='$Erro$',
xlabel='$Interações$'
)
plt.show()
Considere quatro distribuições gaussianas, $C_1, C_2, C_3, C_4$, em um espaço de entrada de dimensionalidade igual a oito, isto é x = ($x_1, x_2, ..., x_8)^t$ .Todas as nuvens de dados formadas têm variâncias unitária, mas centros ou vetores média são diferentes e dados por $m_1 = (0,0,0,0,0,0,0,0)^t , m_2 = (4,0,0,0,0,0,0,0)^t, m_3 = (0,0,0,4,0,0,0,0)^t, m_4 = (0,0,0,0,0,0,0,4)^t $.
Utilize uma rede de autoeconders para reduzir a dimensionalidade dos dados para duas di- mensões. O objetivo é visualizar os dados de dimensão 8 em um espaço de dimensão 2. Esboce os dados neste novo espaço.
Observação: Gere inicialmente os dados em dimensão oito para cada uma das distribuições gaussianas. Selecione o conjunto de treinamento. Defina uma rede de autoencoder com uma arquitetura por exemplo do tipo 8:2:8 ou outro equivalente com mais camadas mas que reduza para 2 dimensões. Após o treinamento faça a redução de dimensionalidade com a rede de arquitetura 8:2 por exemplo.
from tensorflow.keras import Model
# generate four gaussian distributions with 8 dimensions, mean m1 = (0,0,0,0,0,0,0,0), m2 = (4,0,0,0,0,0,0,0), m3 = (0,0,0,4,0,0,0,0), m4 = (0,0,0,0,0,0,0,4) and covariance matrix I
m1 = np.zeros(8)
m2 = np.array([4,0,0,0,0,0,0,0])
m3 = np.array([0,0,0,4,0,0,0,0])
m4 = np.array([0,0,0,0,0,0,0,4])
I = np.eye(8)
x1 = np.random.multivariate_normal(m1, I, 15000)
x2 = np.random.multivariate_normal(m2, I, 15000)
x3 = np.random.multivariate_normal(m3, I, 15000)
x4 = np.random.multivariate_normal(m4, I, 15000)
# plot the data
fig, axes = plt.subplots(ncols=2, figsize=(25, 6))
axes[0].scatter(x1[:,0], x1[:,1], label='Class 1')
axes[0].scatter(x2[:,0], x2[:,1], label='Class 2')
axes[0].scatter(x3[:,4], x3[:,3], label='Class 3')
axes[0].scatter(x4[:,-1], x4[:,-2], label='Class 4')
axes[0].legend()
axes[0].set(
ylabel='$x_2$',
xlabel='$x_1$'
)
plt.show()
# create an autoencoder netork to reduce the dimensionality of the data to 2 and plot the data
input_dim = Input(shape=(8,))
encoded = Dense(8, activation='leaky_relu')(input_dim)
encoded = Dense(4, activation='leaky_relu')(encoded)
encoded = Dense(2, activation='leaky_relu')(encoded)
decoded = Dense(4, activation='leaky_relu')(encoded)
decoded = Dense(8, activation='leaky_relu')(decoded)
autoencoder = Model(input_dim, decoded)
encoder = Model(input_dim, encoded)
opt = tf.keras.optimizers.Adam(learning_rate=0.0001)
autoencoder.compile(optimizer=opt, loss='mean_squared_error')
# fitting the model
history1 = autoencoder.fit(x1, x1, epochs=50, shuffle=True, validation_split=0.1)
history2 = autoencoder.fit(x2, x2, epochs=50, shuffle=True, validation_split=0.1)
history3 = autoencoder.fit(x3, x3, epochs=50, shuffle=True, validation_split=0.1)
history4 = autoencoder.fit(x4, x4, epochs=50, shuffle=True, validation_split=0.1)
Epoch 1/50 422/422 [==============================] - 1s 2ms/step - loss: 0.9627 - val_loss: 0.9539 Epoch 2/50 422/422 [==============================] - 1s 1ms/step - loss: 0.9439 - val_loss: 0.9409 Epoch 3/50 422/422 [==============================] - 1s 1ms/step - loss: 0.9354 - val_loss: 0.9344 Epoch 4/50 422/422 [==============================] - 1s 1ms/step - loss: 0.9297 - val_loss: 0.9282 Epoch 5/50 422/422 [==============================] - 1s 1ms/step - loss: 0.9237 - val_loss: 0.9208 Epoch 6/50 422/422 [==============================] - 1s 1ms/step - loss: 0.9162 - val_loss: 0.9117 Epoch 7/50 422/422 [==============================] - 1s 1ms/step - loss: 0.9075 - val_loss: 0.9017 Epoch 8/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8981 - val_loss: 0.8916 Epoch 9/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8890 - val_loss: 0.8830 Epoch 10/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8812 - val_loss: 0.8763 Epoch 11/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8756 - val_loss: 0.8717 Epoch 12/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8718 - val_loss: 0.8684 Epoch 13/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8688 - val_loss: 0.8657 Epoch 14/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8663 - val_loss: 0.8633 Epoch 15/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8640 - val_loss: 0.8611 Epoch 16/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8617 - val_loss: 0.8589 Epoch 17/50 422/422 [==============================] - 0s 1ms/step - loss: 0.8595 - val_loss: 0.8566 Epoch 18/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8572 - val_loss: 0.8542 Epoch 19/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8549 - val_loss: 0.8519 Epoch 20/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8525 - val_loss: 0.8495 Epoch 21/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8501 - val_loss: 0.8470 Epoch 22/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8477 - val_loss: 0.8446 Epoch 23/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8452 - val_loss: 0.8419 Epoch 24/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8426 - val_loss: 0.8394 Epoch 25/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8399 - val_loss: 0.8368 Epoch 26/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8373 - val_loss: 0.8342 Epoch 27/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8346 - val_loss: 0.8316 Epoch 28/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8319 - val_loss: 0.8289 Epoch 29/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8292 - val_loss: 0.8262 Epoch 30/50 422/422 [==============================] - 1s 2ms/step - loss: 0.8266 - val_loss: 0.8235 Epoch 31/50 422/422 [==============================] - 1s 3ms/step - loss: 0.8239 - val_loss: 0.8208 Epoch 32/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8213 - val_loss: 0.8181 Epoch 33/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8187 - val_loss: 0.8154 Epoch 34/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8159 - val_loss: 0.8127 Epoch 35/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8132 - val_loss: 0.8101 Epoch 36/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8107 - val_loss: 0.8077 Epoch 37/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8082 - val_loss: 0.8051 Epoch 38/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8057 - val_loss: 0.8027 Epoch 39/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8032 - val_loss: 0.8001 Epoch 40/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8008 - val_loss: 0.7975 Epoch 41/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7985 - val_loss: 0.7951 Epoch 42/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7963 - val_loss: 0.7928 Epoch 43/50 422/422 [==============================] - 0s 1ms/step - loss: 0.7941 - val_loss: 0.7906 Epoch 44/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7920 - val_loss: 0.7884 Epoch 45/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7900 - val_loss: 0.7863 Epoch 46/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7879 - val_loss: 0.7844 Epoch 47/50 422/422 [==============================] - 0s 1ms/step - loss: 0.7859 - val_loss: 0.7825 Epoch 48/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7840 - val_loss: 0.7808 Epoch 49/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7823 - val_loss: 0.7794 Epoch 50/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7807 - val_loss: 0.7779 Epoch 1/50 422/422 [==============================] - 1s 1ms/step - loss: 1.5929 - val_loss: 0.9509 Epoch 2/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8839 - val_loss: 0.8212 Epoch 3/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8232 - val_loss: 0.7883 Epoch 4/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8011 - val_loss: 0.7718 Epoch 5/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7901 - val_loss: 0.7633 Epoch 6/50 422/422 [==============================] - 0s 1ms/step - loss: 0.7831 - val_loss: 0.7576 Epoch 7/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7776 - val_loss: 0.7530 Epoch 8/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7732 - val_loss: 0.7494 Epoch 9/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7695 - val_loss: 0.7460 Epoch 10/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7662 - val_loss: 0.7431 Epoch 11/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7634 - val_loss: 0.7406 Epoch 12/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7609 - val_loss: 0.7383 Epoch 13/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7587 - val_loss: 0.7362 Epoch 14/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7569 - val_loss: 0.7346 Epoch 15/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7553 - val_loss: 0.7330 Epoch 16/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7539 - val_loss: 0.7318 Epoch 17/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7527 - val_loss: 0.7308 Epoch 18/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7517 - val_loss: 0.7296 Epoch 19/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7508 - val_loss: 0.7290 Epoch 20/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7501 - val_loss: 0.7283 Epoch 21/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7495 - val_loss: 0.7279 Epoch 22/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7490 - val_loss: 0.7275 Epoch 23/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7486 - val_loss: 0.7271 Epoch 24/50 422/422 [==============================] - 0s 1ms/step - loss: 0.7482 - val_loss: 0.7266 Epoch 25/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7479 - val_loss: 0.7264 Epoch 26/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7476 - val_loss: 0.7259 Epoch 27/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7474 - val_loss: 0.7258 Epoch 28/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7472 - val_loss: 0.7259 Epoch 29/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7470 - val_loss: 0.7253 Epoch 30/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7468 - val_loss: 0.7253 Epoch 31/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7467 - val_loss: 0.7254 Epoch 32/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7465 - val_loss: 0.7250 Epoch 33/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7464 - val_loss: 0.7248 Epoch 34/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7463 - val_loss: 0.7249 Epoch 35/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7462 - val_loss: 0.7247 Epoch 36/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7461 - val_loss: 0.7248 Epoch 37/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7459 - val_loss: 0.7245 Epoch 38/50 422/422 [==============================] - 0s 1ms/step - loss: 0.7459 - val_loss: 0.7244 Epoch 39/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7458 - val_loss: 0.7244 Epoch 40/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7457 - val_loss: 0.7242 Epoch 41/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7456 - val_loss: 0.7241 Epoch 42/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7455 - val_loss: 0.7241 Epoch 43/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7454 - val_loss: 0.7239 Epoch 44/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7453 - val_loss: 0.7240 Epoch 45/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7452 - val_loss: 0.7239 Epoch 46/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7452 - val_loss: 0.7241 Epoch 47/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7451 - val_loss: 0.7236 Epoch 48/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7450 - val_loss: 0.7237 Epoch 49/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7449 - val_loss: 0.7234 Epoch 50/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7449 - val_loss: 0.7235 Epoch 1/50 422/422 [==============================] - 1s 1ms/step - loss: 1.5972 - val_loss: 1.4005 Epoch 2/50 422/422 [==============================] - 1s 1ms/step - loss: 1.3020 - val_loss: 1.1859 Epoch 3/50 422/422 [==============================] - 1s 1ms/step - loss: 1.1143 - val_loss: 1.0354 Epoch 4/50 422/422 [==============================] - 1s 1ms/step - loss: 0.9829 - val_loss: 0.9314 Epoch 5/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8936 - val_loss: 0.8628 Epoch 6/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8432 - val_loss: 0.8324 Epoch 7/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8239 - val_loss: 0.8214 Epoch 8/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8155 - val_loss: 0.8149 Epoch 9/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8100 - val_loss: 0.8099 Epoch 10/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8056 - val_loss: 0.8059 Epoch 11/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8020 - val_loss: 0.8021 Epoch 12/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7989 - val_loss: 0.7989 Epoch 13/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7962 - val_loss: 0.7958 Epoch 14/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7937 - val_loss: 0.7933 Epoch 15/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7915 - val_loss: 0.7911 Epoch 16/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7895 - val_loss: 0.7890 Epoch 17/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7879 - val_loss: 0.7869 Epoch 18/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7863 - val_loss: 0.7852 Epoch 19/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7848 - val_loss: 0.7834 Epoch 20/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7834 - val_loss: 0.7821 Epoch 21/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7821 - val_loss: 0.7806 Epoch 22/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7809 - val_loss: 0.7787 Epoch 23/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7797 - val_loss: 0.7780 Epoch 24/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7787 - val_loss: 0.7763 Epoch 25/50 422/422 [==============================] - 0s 1ms/step - loss: 0.7777 - val_loss: 0.7746 Epoch 26/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7767 - val_loss: 0.7738 Epoch 27/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7759 - val_loss: 0.7720 Epoch 28/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7750 - val_loss: 0.7708 Epoch 29/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7743 - val_loss: 0.7695 Epoch 30/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7735 - val_loss: 0.7687 Epoch 31/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7728 - val_loss: 0.7677 Epoch 32/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7721 - val_loss: 0.7665 Epoch 33/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7715 - val_loss: 0.7657 Epoch 34/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7709 - val_loss: 0.7650 Epoch 35/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7703 - val_loss: 0.7640 Epoch 36/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7697 - val_loss: 0.7637 Epoch 37/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7693 - val_loss: 0.7629 Epoch 38/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7688 - val_loss: 0.7622 Epoch 39/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7683 - val_loss: 0.7616 Epoch 40/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7679 - val_loss: 0.7611 Epoch 41/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7675 - val_loss: 0.7607 Epoch 42/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7670 - val_loss: 0.7599 Epoch 43/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7667 - val_loss: 0.7595 Epoch 44/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7662 - val_loss: 0.7592 Epoch 45/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7658 - val_loss: 0.7587 Epoch 46/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7655 - val_loss: 0.7581 Epoch 47/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7651 - val_loss: 0.7578 Epoch 48/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7647 - val_loss: 0.7573 Epoch 49/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7643 - val_loss: 0.7570 Epoch 50/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7640 - val_loss: 0.7563 Epoch 1/50 422/422 [==============================] - 1s 1ms/step - loss: 2.2073 - val_loss: 1.3175 Epoch 2/50 422/422 [==============================] - 1s 1ms/step - loss: 1.1305 - val_loss: 0.9906 Epoch 3/50 422/422 [==============================] - 1s 1ms/step - loss: 0.9453 - val_loss: 0.8817 Epoch 4/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8663 - val_loss: 0.8280 Epoch 5/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8271 - val_loss: 0.8015 Epoch 6/50 422/422 [==============================] - 1s 1ms/step - loss: 0.8062 - val_loss: 0.7860 Epoch 7/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7931 - val_loss: 0.7751 Epoch 8/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7842 - val_loss: 0.7684 Epoch 9/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7784 - val_loss: 0.7639 Epoch 10/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7746 - val_loss: 0.7613 Epoch 11/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7718 - val_loss: 0.7587 Epoch 12/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7696 - val_loss: 0.7571 Epoch 13/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7678 - val_loss: 0.7551 Epoch 14/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7663 - val_loss: 0.7540 Epoch 15/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7651 - val_loss: 0.7527 Epoch 16/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7639 - val_loss: 0.7518 Epoch 17/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7629 - val_loss: 0.7508 Epoch 18/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7620 - val_loss: 0.7500 Epoch 19/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7612 - val_loss: 0.7491 Epoch 20/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7605 - val_loss: 0.7484 Epoch 21/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7598 - val_loss: 0.7478 Epoch 22/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7592 - val_loss: 0.7472 Epoch 23/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7586 - val_loss: 0.7464 Epoch 24/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7580 - val_loss: 0.7458 Epoch 25/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7574 - val_loss: 0.7452 Epoch 26/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7569 - val_loss: 0.7449 Epoch 27/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7564 - val_loss: 0.7441 Epoch 28/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7559 - val_loss: 0.7439 Epoch 29/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7554 - val_loss: 0.7432 Epoch 30/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7550 - val_loss: 0.7428 Epoch 31/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7546 - val_loss: 0.7424 Epoch 32/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7541 - val_loss: 0.7420 Epoch 33/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7538 - val_loss: 0.7415 Epoch 34/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7534 - val_loss: 0.7411 Epoch 35/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7530 - val_loss: 0.7409 Epoch 36/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7527 - val_loss: 0.7404 Epoch 37/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7522 - val_loss: 0.7400 Epoch 38/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7519 - val_loss: 0.7395 Epoch 39/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7515 - val_loss: 0.7391 Epoch 40/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7512 - val_loss: 0.7388 Epoch 41/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7509 - val_loss: 0.7385 Epoch 42/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7506 - val_loss: 0.7380 Epoch 43/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7504 - val_loss: 0.7377 Epoch 44/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7500 - val_loss: 0.7380 Epoch 45/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7498 - val_loss: 0.7371 Epoch 46/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7495 - val_loss: 0.7368 Epoch 47/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7492 - val_loss: 0.7365 Epoch 48/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7490 - val_loss: 0.7362 Epoch 49/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7487 - val_loss: 0.7360 Epoch 50/50 422/422 [==============================] - 1s 1ms/step - loss: 0.7484 - val_loss: 0.7358
encoded_x1 = encoder.predict(x1)
encoded_x2 = encoder.predict(x2)
encoded_x3 = encoder.predict(x3)
encoded_x4 = encoder.predict(x4)
469/469 [==============================] - 0s 751us/step 469/469 [==============================] - 0s 781us/step 469/469 [==============================] - 0s 789us/step 469/469 [==============================] - 0s 749us/step
# plot history
fig, axes = plt.subplots(ncols=4, figsize=(25, 6))
axes[0].plot(history1.history['loss'], label='Training loss')
axes[0].plot(history1.history['val_loss'], label='Validation loss')
axes[1].plot(history2.history['loss'], label='Training loss')
axes[1].plot(history2.history['val_loss'], label='Validation loss')
axes[2].plot(history3.history['loss'], label='Training loss')
axes[2].plot(history3.history['val_loss'], label='Validation loss')
axes[3].plot(history4.history['loss'], label='Training loss')
axes[3].plot(history4.history['val_loss'], label='Validation loss')
axes[0].legend()
axes[0].set_title('Class 1')
axes[0].set(
ylabel='Loss',
xlabel='Epoch'
)
axes[1].set_title('Class 2')
axes[1].legend()
axes[1].set(
ylabel='Loss',
xlabel='Epoch'
)
axes[2].set_title('Class 3')
axes[2].legend()
axes[2].set(
ylabel='Loss',
xlabel='Epoch'
)
axes[3].set_title('Class 4')
axes[3].legend()
axes[3].set(
ylabel='Loss',
xlabel='Epoch'
)
plt.show()
# plot the data
fig, ax = plt.subplots(figsize=(10,10))
ax.scatter(encoded_x1[:, 0][0:2000], encoded_x1[:, 1][0:2000], label='Classe 1')
ax.scatter(encoded_x2[:, 0][0:2000], encoded_x2[:, 1][0:2000], label='Classe 2')
ax.scatter(encoded_x3[:, 0][0:2000], encoded_x3[:, 1][0:2000], label='Classe 3')
ax.scatter(encoded_x4[:, 0][0:2000], encoded_x4[:, 1][0:2000], label='Classe 4')
ax.legend()
plt.show()
Pesquise sobre redes neurais recorrentes LSTM. Apresente neste estudo aplicações das LSTM deep learning. Seguem abaixo sugestões de aplicações.
As redes neurais LSTM (Long Short-Term Memory) são um tipo específico de redes neurais recorrentes que receberam muita atenção recentemente na comunidade de aprendizado de máquina. De forma geral, as redes LSTM possuem a característica de realimentação, o que permite um efeito de memória de curto e longo prazo. Com isso, a saída é modulada pelo estado dessas células, tornando-se uma propriedade muito importante quando precisamos que a previsão da rede neural dependa do contexto histórico das entradas, e não apenas da última entrada.
Exemplo de uma aplicação
Uma das aplicações das redes neurais LSTM é a predição de séries temporais, isto é, tentar prever o próximo valor a partir de valores anteriores. Assim, escolheu-se um problema onde, dado um ano e um mês, a tarefa é prever o número de passageiros de companhias aéreas internacionais em unidades de 1.000. Os dados variam de janeiro de 1949 a dezembro de 1960, ou 12 anos, com 144 observações.
Ou seja, dado o número de passageiros (em unidades de milhares) neste mês, qual é o número de passageiros no próximo mês?
Você pode escrever uma função simples para converter a única coluna de dados em um conjunto de dados de duas colunas: a primeira coluna contendo a contagem de passageiros deste mês (t) e a segunda coluna contendo a contagem de passageiros do próximo mês (t+1) a ser prevista.
# LSTM for international airline passengers problem with regression framing
import numpy as np
import matplotlib.pyplot as plt
from pandas import read_csv
import math
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense
from tensorflow.keras.layers import LSTM
from sklearn.preprocessing import MinMaxScaler
from sklearn.metrics import mean_squared_error
# convert an array of values into a dataset matrix
def create_dataset(dataset, look_back=1):
dataX, dataY = [], []
for i in range(len(dataset)-look_back-1):
a = dataset[i:(i+look_back), 0]
dataX.append(a)
dataY.append(dataset[i + look_back, 0])
return np.array(dataX), np.array(dataY)
# fix random seed for reproducibility
tf.random.set_seed(7)
# load the dataset
dataframe = read_csv('airline-passengers.csv', usecols=[1], engine='python')
dataset = dataframe.values
dataset = dataset.astype('float32')
# normalize the dataset
scaler = MinMaxScaler(feature_range=(0, 1))
dataset = scaler.fit_transform(dataset)
# split into train and test sets
train_size = int(len(dataset) * 0.67)
test_size = len(dataset) - train_size
train, test = dataset[0:train_size,:], dataset[train_size:len(dataset),:]
print("Train shape: ", train.shape)
print("Test shape: ", test.shape)
Train shape: (96, 1) Test shape: (48, 1)
# reshape into X=t and Y=t+1
look_back = 1
trainX, trainY = create_dataset(train, look_back)
testX, testY = create_dataset(test, look_back)
# reshape input to be [samples, time steps, features]
trainX = np.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1]))
testX = np.reshape(testX, (testX.shape[0], 1, testX.shape[1]))
# create and fit the LSTM network
model = Sequential()
model.add(LSTM(4, input_shape=(1, look_back)))
model.add(Dense(1))
model.compile(loss='mean_squared_error', optimizer='adam')
model.fit(trainX, trainY, epochs=100, batch_size=1, verbose=2)
Epoch 1/100 94/94 - 2s - loss: 0.0431 - 2s/epoch - 24ms/step Epoch 2/100 94/94 - 0s - loss: 0.0229 - 224ms/epoch - 2ms/step Epoch 3/100 94/94 - 0s - loss: 0.0163 - 212ms/epoch - 2ms/step Epoch 4/100 94/94 - 0s - loss: 0.0148 - 232ms/epoch - 2ms/step Epoch 5/100 94/94 - 0s - loss: 0.0140 - 217ms/epoch - 2ms/step Epoch 6/100 94/94 - 0s - loss: 0.0130 - 217ms/epoch - 2ms/step Epoch 7/100 94/94 - 0s - loss: 0.0121 - 217ms/epoch - 2ms/step Epoch 8/100 94/94 - 0s - loss: 0.0112 - 226ms/epoch - 2ms/step Epoch 9/100 94/94 - 0s - loss: 0.0104 - 211ms/epoch - 2ms/step Epoch 10/100 94/94 - 0s - loss: 0.0094 - 220ms/epoch - 2ms/step Epoch 11/100 94/94 - 0s - loss: 0.0084 - 211ms/epoch - 2ms/step Epoch 12/100 94/94 - 0s - loss: 0.0074 - 219ms/epoch - 2ms/step Epoch 13/100 94/94 - 0s - loss: 0.0066 - 221ms/epoch - 2ms/step Epoch 14/100 94/94 - 0s - loss: 0.0057 - 217ms/epoch - 2ms/step Epoch 15/100 94/94 - 0s - loss: 0.0050 - 214ms/epoch - 2ms/step Epoch 16/100 94/94 - 0s - loss: 0.0043 - 214ms/epoch - 2ms/step Epoch 17/100 94/94 - 0s - loss: 0.0037 - 220ms/epoch - 2ms/step Epoch 18/100 94/94 - 0s - loss: 0.0032 - 216ms/epoch - 2ms/step Epoch 19/100 94/94 - 0s - loss: 0.0029 - 210ms/epoch - 2ms/step Epoch 20/100 94/94 - 0s - loss: 0.0026 - 220ms/epoch - 2ms/step Epoch 21/100 94/94 - 0s - loss: 0.0024 - 212ms/epoch - 2ms/step Epoch 22/100 94/94 - 0s - loss: 0.0022 - 226ms/epoch - 2ms/step Epoch 23/100 94/94 - 0s - loss: 0.0021 - 208ms/epoch - 2ms/step Epoch 24/100 94/94 - 0s - loss: 0.0020 - 218ms/epoch - 2ms/step Epoch 25/100 94/94 - 0s - loss: 0.0021 - 217ms/epoch - 2ms/step Epoch 26/100 94/94 - 0s - loss: 0.0020 - 208ms/epoch - 2ms/step Epoch 27/100 94/94 - 0s - loss: 0.0020 - 220ms/epoch - 2ms/step Epoch 28/100 94/94 - 0s - loss: 0.0020 - 215ms/epoch - 2ms/step Epoch 29/100 94/94 - 0s - loss: 0.0021 - 219ms/epoch - 2ms/step Epoch 30/100 94/94 - 0s - loss: 0.0020 - 210ms/epoch - 2ms/step Epoch 31/100 94/94 - 0s - loss: 0.0020 - 222ms/epoch - 2ms/step Epoch 32/100 94/94 - 0s - loss: 0.0021 - 221ms/epoch - 2ms/step Epoch 33/100 94/94 - 0s - loss: 0.0021 - 213ms/epoch - 2ms/step Epoch 34/100 94/94 - 0s - loss: 0.0020 - 214ms/epoch - 2ms/step Epoch 35/100 94/94 - 0s - loss: 0.0021 - 213ms/epoch - 2ms/step Epoch 36/100 94/94 - 0s - loss: 0.0020 - 224ms/epoch - 2ms/step Epoch 37/100 94/94 - 0s - loss: 0.0020 - 207ms/epoch - 2ms/step Epoch 38/100 94/94 - 0s - loss: 0.0020 - 213ms/epoch - 2ms/step Epoch 39/100 94/94 - 0s - loss: 0.0020 - 219ms/epoch - 2ms/step Epoch 40/100 94/94 - 0s - loss: 0.0020 - 223ms/epoch - 2ms/step Epoch 41/100 94/94 - 0s - loss: 0.0020 - 216ms/epoch - 2ms/step Epoch 42/100 94/94 - 0s - loss: 0.0020 - 216ms/epoch - 2ms/step Epoch 43/100 94/94 - 0s - loss: 0.0020 - 212ms/epoch - 2ms/step Epoch 44/100 94/94 - 0s - loss: 0.0020 - 210ms/epoch - 2ms/step Epoch 45/100 94/94 - 0s - loss: 0.0021 - 216ms/epoch - 2ms/step Epoch 46/100 94/94 - 0s - loss: 0.0019 - 229ms/epoch - 2ms/step Epoch 47/100 94/94 - 0s - loss: 0.0020 - 216ms/epoch - 2ms/step Epoch 48/100 94/94 - 0s - loss: 0.0021 - 216ms/epoch - 2ms/step Epoch 49/100 94/94 - 0s - loss: 0.0020 - 211ms/epoch - 2ms/step Epoch 50/100 94/94 - 0s - loss: 0.0020 - 219ms/epoch - 2ms/step Epoch 51/100 94/94 - 0s - loss: 0.0020 - 213ms/epoch - 2ms/step Epoch 52/100 94/94 - 0s - loss: 0.0020 - 209ms/epoch - 2ms/step Epoch 53/100 94/94 - 0s - loss: 0.0020 - 211ms/epoch - 2ms/step Epoch 54/100 94/94 - 0s - loss: 0.0020 - 219ms/epoch - 2ms/step Epoch 55/100 94/94 - 0s - loss: 0.0020 - 210ms/epoch - 2ms/step Epoch 56/100 94/94 - 0s - loss: 0.0020 - 215ms/epoch - 2ms/step Epoch 57/100 94/94 - 0s - loss: 0.0020 - 213ms/epoch - 2ms/step Epoch 58/100 94/94 - 0s - loss: 0.0020 - 214ms/epoch - 2ms/step Epoch 59/100 94/94 - 0s - loss: 0.0020 - 219ms/epoch - 2ms/step Epoch 60/100 94/94 - 0s - loss: 0.0020 - 212ms/epoch - 2ms/step Epoch 61/100 94/94 - 0s - loss: 0.0020 - 217ms/epoch - 2ms/step Epoch 62/100 94/94 - 0s - loss: 0.0021 - 213ms/epoch - 2ms/step Epoch 63/100 94/94 - 0s - loss: 0.0020 - 211ms/epoch - 2ms/step Epoch 64/100 94/94 - 0s - loss: 0.0020 - 221ms/epoch - 2ms/step Epoch 65/100 94/94 - 0s - loss: 0.0020 - 224ms/epoch - 2ms/step Epoch 66/100 94/94 - 0s - loss: 0.0020 - 217ms/epoch - 2ms/step Epoch 67/100 94/94 - 0s - loss: 0.0021 - 209ms/epoch - 2ms/step Epoch 68/100 94/94 - 0s - loss: 0.0020 - 219ms/epoch - 2ms/step Epoch 69/100 94/94 - 0s - loss: 0.0020 - 209ms/epoch - 2ms/step Epoch 70/100 94/94 - 0s - loss: 0.0020 - 214ms/epoch - 2ms/step Epoch 71/100 94/94 - 0s - loss: 0.0020 - 214ms/epoch - 2ms/step Epoch 72/100 94/94 - 0s - loss: 0.0020 - 216ms/epoch - 2ms/step Epoch 73/100 94/94 - 0s - loss: 0.0020 - 222ms/epoch - 2ms/step Epoch 74/100 94/94 - 0s - loss: 0.0021 - 229ms/epoch - 2ms/step Epoch 75/100 94/94 - 0s - loss: 0.0020 - 227ms/epoch - 2ms/step Epoch 76/100 94/94 - 0s - loss: 0.0020 - 211ms/epoch - 2ms/step Epoch 77/100 94/94 - 0s - loss: 0.0019 - 218ms/epoch - 2ms/step Epoch 78/100 94/94 - 0s - loss: 0.0020 - 216ms/epoch - 2ms/step Epoch 79/100 94/94 - 0s - loss: 0.0020 - 209ms/epoch - 2ms/step Epoch 80/100 94/94 - 0s - loss: 0.0020 - 211ms/epoch - 2ms/step Epoch 81/100 94/94 - 0s - loss: 0.0019 - 216ms/epoch - 2ms/step Epoch 82/100 94/94 - 0s - loss: 0.0021 - 220ms/epoch - 2ms/step Epoch 83/100 94/94 - 0s - loss: 0.0020 - 211ms/epoch - 2ms/step Epoch 84/100 94/94 - 0s - loss: 0.0019 - 217ms/epoch - 2ms/step Epoch 85/100 94/94 - 0s - loss: 0.0020 - 214ms/epoch - 2ms/step Epoch 86/100 94/94 - 0s - loss: 0.0020 - 223ms/epoch - 2ms/step Epoch 87/100 94/94 - 0s - loss: 0.0021 - 235ms/epoch - 2ms/step Epoch 88/100 94/94 - 0s - loss: 0.0020 - 231ms/epoch - 2ms/step Epoch 89/100 94/94 - 0s - loss: 0.0020 - 213ms/epoch - 2ms/step Epoch 90/100 94/94 - 0s - loss: 0.0020 - 217ms/epoch - 2ms/step Epoch 91/100 94/94 - 0s - loss: 0.0020 - 228ms/epoch - 2ms/step Epoch 92/100 94/94 - 0s - loss: 0.0020 - 210ms/epoch - 2ms/step Epoch 93/100 94/94 - 0s - loss: 0.0020 - 226ms/epoch - 2ms/step Epoch 94/100 94/94 - 0s - loss: 0.0020 - 209ms/epoch - 2ms/step Epoch 95/100 94/94 - 0s - loss: 0.0021 - 216ms/epoch - 2ms/step Epoch 96/100 94/94 - 0s - loss: 0.0020 - 219ms/epoch - 2ms/step Epoch 97/100 94/94 - 0s - loss: 0.0020 - 214ms/epoch - 2ms/step Epoch 98/100 94/94 - 0s - loss: 0.0020 - 215ms/epoch - 2ms/step Epoch 99/100 94/94 - 0s - loss: 0.0020 - 213ms/epoch - 2ms/step Epoch 100/100 94/94 - 0s - loss: 0.0020 - 221ms/epoch - 2ms/step
<keras.callbacks.History at 0x7f663c5adb10>
# make predictions
trainPredict = model.predict(trainX)
testPredict = model.predict(testX)
3/3 [==============================] - 0s 4ms/step 2/2 [==============================] - 0s 5ms/step
# invert predictions
trainPredict = scaler.inverse_transform(trainPredict)
trainY = scaler.inverse_transform([trainY])
testPredict = scaler.inverse_transform(testPredict)
testY = scaler.inverse_transform([testY])
# calculate root mean squared error
trainScore = np.sqrt(mean_squared_error(trainY[0], trainPredict[:,0]))
print('Train Score: %.2f RMSE' % (trainScore))
testScore = np.sqrt(mean_squared_error(testY[0], testPredict[:,0]))
print('Test Score: %.2f RMSE' % (testScore))
Train Score: 22.68 RMSE Test Score: 49.34 RMSE
# shift train predictions for plotting
trainPredictPlot = np.empty_like(dataset)
trainPredictPlot[:, :] = np.nan
trainPredictPlot[look_back:len(trainPredict)+look_back, :] = trainPredict
# shift test predictions for plotting
testPredictPlot = np.empty_like(dataset)
testPredictPlot[:, :] = np.nan
testPredictPlot[len(trainPredict)+(look_back*2)+1:len(dataset)-1, :] = testPredict
# plot baseline and predictions
plt.plot(scaler.inverse_transform(dataset))
plt.plot(trainPredictPlot)
plt.plot(testPredictPlot)
plt.show()
Apresente um estudo sobre transferência de conhecimento (transfer learning) no contexto de deep learning.
De acordo com Brownlee (2019), Transfer Learning é um método de aprendizagem de máquina no qual permite que um modelo treinado para uma determinada tarefa seja utilizado como um ponto de partida de um modelo para outro problema com características similares.
Esta técnica é bastante utilizada em tarefas de visão computacional, processamento de linguagem natural, dados os vastos recursos computacionais (principalmente as GPUs) e tempo necessários para desenvolver modelos de rede neural sobre esses problemas, além das emissões de CO2 causadas pelo gasto de energia. Além disso, é possível encontrar modelos treinados por grandes empresas por muitas horas e com uma grande infraestrutura disponíveis de forma gratuita na internet. Isso permite obter excelentes resultados com um tempo de treinamento muito menor do que seria treinar um novo modelo do zero.
É possível utilizar esta técnica a partir dos três passos a seguir:
Selecione Modelo pré-treinado: Escolha um modelo de origem pré-treinado dentre os modelos disponíveis. Muitas instituições de pesquisa lançam modelos em conjuntos de dados grandes e desafiadores que podem ser incluídos no conjunto de modelos candidatos a serem escolhidos.
Modelo de Reutilização: Utiliza o modelo pré-treinado como ponto de partida para um modelo na segunda tarefa de interesse. Isso pode envolver o uso de todo ou de partes do modelo, dependendo da técnica de modelagem utilizada.
Modelo de sintonia: Opcionalmente, o modelo pode precisar ser adaptado ou refinado nos dados do par de entrada-saída disponíveis para a tarefa de interesse. Assim, você pode adicionar mais camadas ao final da rede para adptar ao seu problema.
Exemplos de modelos pré-treinados na área de visão computacional:
Exemplos de modelos pré-treinados na área de processamento de linguagem natural: